- On Lie algebras and some special functions of mathematical
physics, AMS Memoir no. 50, Providence, 1964.
- Some applications of the representation theory of the Euclidean
group in three-space, Comm. Pure Appl. Math., 17 (1964), pp.
527-540. PDF
- On a generalization of Bessel functions, Comm. Pure Appl. Math.,
18 (1965), pp. 393-399.
- The special function theory of occupation number space, Comm.
Pure Appl. Math., 18 (1965), pp. 679-696.
- The special function theory of occupation number space II, Comm.
Pure Appl. Math., l9 (l966), pp. 125-138.
- A branching law for the symplectic groups, Pacific Journal of
Math., l6 (1966), pp. 341-346.
PDF
- Confluent hypergeometric functions and representations of a
four-parameter Lie group, Comm. Pure Appl. Math., l9 (l966), pp.
251-259.
- Lie
Theory and Special Functions, Academic Press (1968), a monograph of
about 350 pages.
- Special functions and the complex Euclidean group in 3-space, I,
J. Math. Phys. 9 (1968), pp. 1163-1175. PDF
- Special functions and the complex Euclidean group in 3-space,
II, J. Math. Phys. 9(1968), pp. 1176-1187. PDF
- Lie theory and the hypergeometric functions, J. Math. Mech., 17
(1968), pp. 1143-1174.
- Special functions and the complex Euclidean group in 3-space,
III, J. Math. Phys. 9 (1968), pp. 1434-1444. PDF
- Lie theory and difference equations, I, J. Math. Anal. Appl., 28
(1969), pp. 383-399.
- Lie theory and q-difference equations, in Studies in
Applied Mathematics 6, Special Functions and Wave Propagation, SIAM
Philadelphia, 1970.
- Lie theory and q-difference equations, SIAM J. Math.
Anal., 1(1970), pp. 171-188. (not identical to 14) PDF
- Lie theory and special functions satisfying second order
nonhomogeneous differential equations, SIAM J. Math. Anal., 1(1970),
pp. 246-265. PDF
- Lie theory and some special solutions of the hypergeometric
equation, SIAM J. Math. Anal., 1(1970), pp. 405-425. PDF
- Invariant
tensor fields in physics and the classical groups, SIAM J. Appl.
Math. 20(1971), pp. 503-519.
- On Lie algebras of difference operators and the special
functions of mathematical physics, SIAM J. Math. Anal. 2 (1971), pp.
307-327. PDF
- Lie theory and difference equations, II, J. Math. Anal. Appl. 39
(1972), pp. 406-422.
- Symmetry
Groups and Their Applications, (a textbook of about 500 pages)
Academic Press, 1972 in the Pure and Applied Mathematics Series, edited
by Eilenberg and Smith.
- Clebsch-Gordan coefficients and special function identities, I.
The Harmonic oscillator group, J. Math. Phys. 13 (1972), pp.
648-655. PDF
- Clebsch-Gordan coefficients and special function identities, II.
The rotation and Lorentz groups, J. Math. Phys. 13 (1972), pp.
827-833. PDF
- Lie theory and generalized hypergeometric functions, SIAM J.
Math. Anal. 3 (1972), pp. 31-44. PDF
- Symmetries of differential equations. The hypergeometric and
Euler-Darboux equations, SIAM J. Math. Anal. 4 (1973), pp. 314-328. PDF
- Lie theory and the Appell function F1 , SIAM J. Math.
Anal. 4 (1973), pp. 638-655. PDF
- Lie theory and the Lauricella functions FD , J. Math.
Phys. 13 (1972), pp. 1393-1399. PDF
- Lie
theory and generalizations of the hypergeometric functions, SIAM J.
Appl. Math. 25 (1973), pp. 226-235.
- Lie algebras and generalizations of the hypergeometric function,
Proceedings of the AMS Summer Institute (1972), Harmonic Analysis on
homogeneous spaces. Proceedings of Symposia in Pure Mathematics, Vol.
XXVI, AMS, Providence, R.I., 1973. PDF
- Lie theory and Meijer's G-function, SIAM J. Math. Anal.
5 (1974), pp. 309-318. PDF
- Lie theory and separation of variables. I. Parabolic cylinder
coordinates, SIAM J. Math. Anal. 5 (1974), pp. 626-643. PDF
- Lie theory and separation of variables. II. Parabolic
coordinates, SIAM J. Math. Anal. 5 (l974), pp. 822-836. PDF
- Lie theory and separation of variables. III. The equation Ftt-Fss=k2F,
with E. G. Kalnins. J. Math. Phys. l5 (1974), pp. 1025-1032, Erratum,
16 (1975), p. 1531. PDF
- Lie theory and separation of variables. IV. The groups SO(2,1)
and SO(3) , with E.G. Kalnins. J. Math. Phys. 15 (1974), pp.
1263-74. PDF
- Complete sets of commuting operators and O(3) scalars in the
enveloping algebra of SU(3) , with B. Judd, J. Patera and P.
Winternitz. J. Math. Phys. 15 (1974), pp. 1787-1799. PDF
- Lie theory and separation of variables. V. The equations iUt
+ Uxx = 0 and iUt + Uxx - (c/x2)U
= 0, with E.G. Kalnins. J. Math. Phys. 15 (1974), pp. 1728-1737. PDF
- Lie theory and separation of variables. VI. The equation iUt
+Uxx+ Uyy = 0, with C.P. Boyer and E.G. Kalnins. J. Math. Phys. 16 (1975), pp.
499-511.
- A classification of second order raising operators for
Hamiltonians in two variables, with C.P. Boyer, J. Math. Phys. 15
(1974), pp. 1484-1489. PDF
- Symmetry and separation of variables for the heat equation,
with E.G. Kalnins. Proceedings of Conference on Symmetry, Similarity
and
Group-Theoretic Methods in Mechanics, Calgary, 1974.
- The group O(4) , separation of variables and the hydrogen atom,
with E.G. Kalnins and P. Winternitz, SIAM
J. Appl. Math. 30 (1976), pp. 630-664.
- Lie theory and separation of variables. VII. The Harmonic
oscillator in elliptic coordinates and Ince polynomials, with C.P.
Boyer and E.G. Kalnins. J.
Math. Phys. 16 (1975), pp. 512-517.
- Lie theory and separation of variables. VIII. Semi-subgroup
coordinates for
Ott - \Delta2 O=
0, with E.G. Kalnins, J.
Math. Phys. 16 (1975), pp. 2507-2516.
- Lie theory and separation of variables IX. Orthogonal
R-separable coordinate systems for the wave equation \Psitt
- \Delta2\Psi = 0, with E.G. Kalnins, J. Math. Phys., 17 (1976),
pp. 331-355.
- Lie theory and separation of variables. X. Nonorthogonal
R-separable solutions of the wave equation
Ott=
\Delta2O , with E.G. Kalnins, J. Math. Phys. 17 (1976),
pp. 356-368.
- Lie theory and separation of variables. XI. The
Euler-Poisson-Darboux equation, with E.G. Kalnins, J. Math. Phys. 17 (1976),
pp. 369-377.
- Symmetry
and Separation of Variables, Addison-Wesley, Reading, Mass. (1977).
- Symmetry, separation of variables and special functions, in
Theory and Application of Special Functions, R. Askey, ed., Proceedings
of an Advanced Seminar conducted from March 31-April 2, 1975, Academic
Press, New York, 1975.
- Symmetry and separation of variables for the Helmholtz and
Laplace equations, with C.P. Boyer and E.G. Kalnins, Nagoya Math. J. 60
(1976), pp. 35-80. PDF
- Lie Theory and Special Functions, (translation of publication 8
into Japanese, A. Orihara, translator) Sangyo Tosho Publishing Company,
Tokyo.
- Lie theory and the wave equation in space time. 1. The Lorentz
group, with E.G. Kalnins, J.
Math. Phys. 18 (1977), pp. 1-16.
- Lie theory and the wave equation in space time. 2. The group
SO(4,C), with E.G. Kalnins, SIAM J. Math. Anal. 9 (1978), pp. 12-33. PDF
- Lie theory and the wave equation in space time. 3. Semisubgroup
coordinates, with E.G. Kalnins, J. Math. Phys. 18 (1977),
pp. 271-280.
- Lie theory and the wave equation in space time. 4. The
Klein-Gordan equation, with E.G. Kalnins, J. Math. Phys. 19 (1978),
pp. 1233-1246.
- Lie theory and the wave equation in space time. 5. Orthogonal
coordinates, with E.G. Kalnins, J. Math. Phys. 19 (1978),
pp. 1247-1257.
- Symmetry and separation of variables for linear differential and
Hamilton-Jacobi equations, in Group Theoretical Methods in Physics,
Proceedings of Symposium on Group Theoretic Methods in Physics,
Montreal, 1976, Academic Press, New York 1977.
- A relationship between Lie theory and continued fraction
expansions for special functions, with C.P. Boyer, in Pad'e and
Rational Approximation, Academic Press, New York, 1977.
- Separable coordinates for three-dimensional complex Riemannian
spaces, with E.G. Kalnins, J. Diff. Geometry, 14 (1979), pp. 221-236.
- Symmetry and separation of variables for the Hamilton-Jacobi
equation (Wt)2 - (Wx)2-
(Wy)2 = 0, with C.P. Boyer and E.G. Kalnins, J. Math. Phys. 19 (1978),
pp. 200-211.
- R-separable
coordinates for three-dimensional complex Riemannian spaces, with
C.P. Boyer and E.G. Kalnins, T.A.M.S. 242 (1978), pp. 355-376.
- The wave equation, O(2,2) , and separation of variables
on hyperboloids, with E.G. Kalnins, Proceedings of the Royal Society of
Edinburgh 79A (1977), pp. 227-256. PDF
- R-separation
of variables for the four-dimensional flat space Laplace and
Hamilton-Jacobi equation, with E.G. Kalnins, T.A.M.S. 244 (1979),
pp. 241-261.
- The wave equation and separation of variables on the complex
sphere S4, with E.G. Kalnins, J. Math. Anal. Appl.
83 (1981) 449-469. PDF
- Separable coordinates for four-dimensional Riemannian spaces,
with C.P. Boyer and E.G. Kalnins, Commun. Math. Phys. 59 (l978), pp.
285-302. PDF
- Nonorthogonal separable coordinate systems for the flat 4-space
Helmholtz equation, with E.G. Kalnins, J. Phys. A: Math. Gen. 12
(1979), pp. 1129-1147.
- Symmetry and variable separation for the Helmholtz, wave and
Hamilton-Jacobi equations, Proceedings of 1979 Einstein Symposium:
Symmetry in Physics, Southern Illinois University, in Symmetries in
Science, B. Gruber and R.S. Millman, Ed., Plenum, New York, 1980.
- Nonorthogonal R-separable coordinates for four
dimensional complex Riemannian spaces, with E.G. Kalnins, J. Math. Phys. 22 (1981)
pp. 42-50.
- The Lie theory of two-variable hypergeometric functions, with
H.L. Manocha and E.G. Kalnins, Studies in Applied Mathematics, 62
(l980), pp. 143-173. PDF
- Transformation and reduction formulas for two-variable
hypergeometric functions on the sphere S2, with H.L.
Manocha and E.G. Kalnins, Studies in Applied Mathematics, 63 (l980),
pp. 155-167. PDF
- Harmonic analysis and expansion formulas for two-variable
hypergeometric functions, with H.L. Manocha and E.G. Kalnins, Studies
in Applied Mathematics 66 (1982), pp. 69-89. PDF
- Subgroups of Lie groups and separation of variables, with J.
Patera and P. Winternitz, J. Math. Phys. 22 (1981),
pp.
251-260.
- Killing tensors and variable separation for Hamilton-Jacobi
and Helmholtz equations, with E.G. Kalnins, SIAM J. Math. Anal. 11
(1980),
pp. 1011-1026. PDF
- Killing tensors and nonorthogonal variable separation for the
Hamilton-Jacobi equation, with E.G. Kalnins, SIAM J. Math. Anal. 12
(1981), pp. 617- 638. PDF
- Conformal Killing tensors and variable separation for the
Hamilton-Jacobi equation, with E.G. Kalnins, SIAM J. Math. Anal.,14
(1983), pp. 126-137. PDF
- Killing tensors and variable separation for Hamilton-Jacobi
equations, Proceedings of Symposium on Group Theoretic Methods in
Physics,
Cocoyoc, Mexico, June, 1980, Springer-Verlag, 1982.
- Separation of variables in Einstein spaces I. Two ignorable
and one null coordinate, with C.P. Boyer and E.G. Kalnins, J. Phys. A: Math Gen. 14
(1981), pp. 1675-1684.
- Some remarkable R-separable coordinate systems for the
Helmholtz equation, with E.G. Kalnins, Letters in Math. Phys. 4 (1980),
pp. 469-474.
- The general theory of R-separation for Helmholtz
equations, with E.G. Kalnins, J. Math. Phys. 24 (1983),
pp. 1047-1053.
- Nonpolynomial constants of the motion and partial separation of
the Hamilton-Jacobi equation, with E.G. Kalnins, Applicable Analysis 13
(1982) pp. 127-137.
- Intrinsic characterization of orthogonal R-separation
for Laplace equations, with E.G. Kalnins, J. Phys. A. Math. Gen. 15
(1982), pp. 2699-2709. PDF
- Intrinsic characterization of orthogonal separation of one
coordinate in the Hamilton-Jacobi equation, with E.G. Kalnins, J. Phys. A: Math. Gen. 15
(1982), pp. 2003-2011.
- Symmetry Groups and Their Applications, (translation of
publication 21 into Chinese, Luan Dehai translator) 1981.
- Symmetry and Separation of Variables, (translation of
publication 46 into Russian) 1981.
- Intrinsic characterization of variable separation for
Hamilton-Jacobi and Helmholtz equations, Proceedings of International
Symposium on Algebra and its Applications, New Delhi, 1981, Algebra and
its Applications, Lecture Notes in Pure and Applied Mathematics, Vol.
91, Dekker, New York 1984.
- Intrinsic characterization of variable separation for the
partial differential equations of mechanics, with E.G. Kalnins,
Proceedings of Symposium on Modern Developments in Analytical
Mechanics, Torino, 1982, Acta Academiae Scientiarum Taurinensis, Torino
1983. PDF
- The technique of variable separation for partial differential
equations, Proceedings of School and Workshop on Nonlinear Phenomena,
Oaxtepec, Mexico, November 29- December 17, 1982, Lecture Notes in
Physics, Vol.
189, pp. 184-208, Springer-Verlag, New York 1983.
- The theory of orthogonal R-separation for Helmholtz equations,
with E.G. Kalnins, Advances in Mathematics, 51 (1984), pp.
91-106. PDF
- Separation
of variables on n-dimensional Riemannian manifolds 1. The n-sphere Sn
and Euclidean n-space Rn, with E.G. Kalnins, J. Math.
Phys., 27 (1986), pp. 1721-1736.
- Separation of variables on n-dimensional Riemannian
manifolds 2. The n-dimensional hyperboloid Hn, with
E.G. Kalnins, University of Waikato Research Report 103. (The contents
of this paper were published in the book by E. G. Kalnins, Separation
of Variables for Riemannian Spaces of Constant Curvature, Pitman,
Monographs and Surveys in Pure and Applied Mathematics, Longman, Essex,
England 1986.)
- Separation of variables on n-dimensional Riemannian
manifolds 3. Conformally Euclidean spaces Cn, with
E.G. Kalnins, University of Waikato Research Report 105. (The contents
of this paper were published in the book by E. G. Kalnins, Separation
of Variables for Riemannian Spaces of Constant Curvature, Pitman,
Monographs and Surveys in Pure and Applied Mathematics, Longman, Essex,
England 1986.)
- Related evolution equations and Lie symmetries, with E.G.
Kalnins. SIAM J. Math. Anal., 16 (1985), pp. 221-232. PDF
- Stäckel - equivalent integrable Hamiltonian
systems, with C.P.
Boyer and E.G. Kalnins. SIAM J. Math. Anal., 17 (1986), pp.
778-797. PDF
- Separation
of variables for complex Riemannian spaces of constant curvature. I.
Orthogonal separable coordinates for Snc and Enc,
with E.G. Kalnins and G.J. Reid, Proc. R. Soc. Lond. A 394 (1984), pp.
183-206.
- Differential-Stäckel
matrices, with E.G. Kalnins, J. Math. Phys., 26 (1985), pp.
1560-1565.
- Generalized
Stäckel matrices, with E.G. Kalnins, J. Math. Phys.,
26 (1985), pp.
2168-2173.
- R-separation
of variables for the time-dependent Hamilton-Jacobi and
Schrödinger
equations, with E.G. Kalnins, J.Math. Phys., 28 (1987), pp.
1005-1015.
- Matrix
operator symmetries of the Dirac equation and separation of variables,
with E.G. Kalnins and G.C. Williams, J. Math. Phys. 27 (1986), pp.
1893-1900.
- Canonical equations and symmetry techniques for q-series,
with A.J. Agarwal and E.G. Kalnins, SIAM J. Math Anal., 18 (1987), pp.
1519-1538. PDF
- Nonorthogonal separable coordinates for Sn
and En, with E.G. Kalnins, University of Waikato
Research Report.
- Equivalence classes of related evolution equations and Lie
symmetries, with E.G. Kalnins, J. Phys. A: Math. Gen., 20
(1987), pp. 5435-5446.
- Electromagnetic
waves in Kerr geometry, with E.G. Kalnins, Proc. R. Soc. Lond. A
408 (1986), pp. 23-30.
- Symmetry techniques for q-series: Askey-Wilson
polynomials, with E.G. Kalnins, Rocky Mountain Mathematics Journal 19
(1989), pp. 223-230. PDF
- A note on Wilson polynomials, SIAM J. Math. Anal., 18 (1987),
pp. 1221-1226. PDF
- q-series and orthogonal polynomials associated with
Barnes' first lemma, with E.G. Kalnins, SIAM J. Math. Anal. 19 (1988),
pp. 1216-1231. PostScript
- Mechanisms for variable separation in partial differential
equations and their relationship to group theory, Proceedings of School
on Symmetry and Nonlinear Phenomena, Paipa, Colombia, February 22-26,
1988, pp. 188-221, in Symmetries and Nonlinear Phenomena, D. Levi
and P. Winternitz, eds., World Scientific, London, 1989. Postscript file
- Separation of variables methods for systems of differential
equations in mathematical physics, with E. G. Kalnins, in the volume
"Lie
Theory, Differential Equations and Representation Theory", V. Hussin,
ed.,
CRM, Montreal 1990. Postscript file
- Conformal symmetries and generalized recurrences for heat and
Schrödinger equations in one spatial dimension, with E.G.
Kalnins and
R.D. Levine, pp. 237-256, in the volume "Mechanics, Analysis and
Geometry: 200 years after Lagrange", M. M. Francaviglia, ed., North
Holland, Amsterdam 1991. PostScript
- Symmetry techniques and orthogonality for q-series, in q-Series
and Partitions, D. Stanton, ed., IMA Volumes in Mathematics and its
Applications, Vol. 18, Springer-Verlag, New York, 1989. Postscript file
- Killing
Yano tensors and variable separation in Kerr geometry, with E.G.
Kalnins and G.C. Williams, J. Math Phys. 30 (1989), pp. 2360-2365.
- Teukolsky-Starobinsky identities for arbitrary spin, with E.G.
Kalnins and G.C. Williams, J. Math. Phys. 30 (1989), pp. 2925-2929. PostScript
- Families of orthogonal and biorthogonal polynomials on the n-sphere,
with E.G. Kalnins and M. Tratnik, SIAM J. Math. Anal. 22, (1991) pp.
272-294. PostScript
- Complete
sets of functions for perturbations of Robertson Walker cosmologies,
with E.G. Kalnins, J. Math. Phys. 32, (1991), pp. 698-707.
- Topics in harmonic analysis with applications to RADAR and
SONAR, in RADAR and SONAR, Part I, by R. Blahut, W. Miller and C.
Wilcox, IMA Volumes in Mathematics and its Applications,
Springer-Verlag, New York, 1991. PDFPostScript
- Hypergeometric expansions of Heun polynomials, with E.G.
Kalnins, SIAM J. Math. Anal. 22, (1991) pp. 1450-1459. PostScript
- Orthogonal polynomials on n-spheres: Gegenbauer, Jacobi
and Heun, with E.G. Kalnins, in Topics in Polynomials of One and
Several Variables and their Applications: A Legacy of P.L. Chebyshev
(1821-1894), H.M. Srivastava, T.M. Rassias and A. Yanushauskas, eds.,
World Scientific, Singapore, 1991. PostScript
- A note on group contractions and radar ambiguity functions,
with E.G. Kalnins, in RADAR and SONAR, Part II, M. Bernfeld, R. Blahut
and A. Grunbaum, eds., IMA Volumes in Mathematics and its Applications,
Springer-Verlag, New York, 1992. PostScript
- Series solutions for the Dirac equation in Kerr Newman space
time, with E.G. Kalnins, J. Math. Phys. 32, (1991), pp. 1415-1423. PostScript
- Models of q-algebra representations: Tensor products
of special unitary and oscillator algebras, with E.G. Kalnins and H.L.
Manocha, J. Math. Phys. 33, (1992), pp. 2365-2383. PostScript
- Separable coordinates, integrability and the Niven equations,
with E.G. Kalnins, J. Phys. A: Math. Gen. 25, (1992), pp. 5663-5675. PostScript
- Models of q-algebra representations: The group of plane
motions, with E.G. Kalnins and Sanchita Mukherjee, SIAM J. Math. Anal.
25, (1994), pp. 513-527. PostScript
- Recent advances in the use of separation of variables methods in
general relativity,with E.G. Kalnins and G.C. Williams, Phil. Trans.
R. Soc. Lond. A 340, (1992), pp. 337-352. PostScript
- Recent advances in the use of separation of variables methods in
general relativity, with E.G. Kalnins and G.C. Williams, in the book
"Classical General Relativity", S. Chandrasekhar, Editor, Oxford
University
Press 1993, pp. 1-16. PostScript
- Models of q-algebra representations: Matrix elements
of Uq(su2), with E.G. Kalnins and
Sanchita Mukherjee, in "Lie algebras, cohomology and new applications
to quantum mechanics", a volume in the Contemporary Mathematics Series,
American Mathematical Society, Providence RI 1994. PostScript
- Models of q-algebra representations: Matrix elements
of the q-oscillator algebra, with E.G. Kalnins and Sanchita
Mukherjee, J. Math. Phys. 43, (1993), pp. 5333-5356. PostScript
- Functional separation of variables for Laplace equations in
two dimensions, with Lee Rubel, J. Phys. A: Math. Gen. 26, (1993) pp.
1901-1913. PostScript
- Quadrics on complex Riemannian spaces of constant curvature,
separation of variables and the Gaudin magnet, with E.G. Kalnins and
V.B. Kuznetsov, J. Math. Phys. 35, (1994), 1710-31. PostScript
- Models of q-algebra representations: q-integral
transforms and ``addition theorems'', with E.G. Kalnins, J. Math. Phys.
35, (1994), 1951-75. PostScript
- Intrinsic characterization of the separation constant for spin 1
and gravitational perturbations in Kerr geometry, with E.G. Kalnins,
and G.C. Williams, Trans. R. Soc. Lond. A439. (1996), 997. PostScript
- q-algebra representations of the Euclidean,
pseudo-Euclidean and oscillator algebras, and their tensor products,
with E.G. Kalnins, in "Symmetries and Integrability of Difference
Equations", Decio Levi editor, CRM Proc. Lect. Notes, American
Mathematical Society, Providence, RI 1996. PDFPostScript
- Separation of variables and the XXZ Gaudin magnet, with
E.G. Kalnins and V.B. Kuznetsov, Rendiconti Seminario Matematico
dell'Universita' e del Politecnico di Torino, Volume 53, no. 2 (1995),
109-120. PostScript
- A note on tensor products of q-algebra representations
and orthogonal polynomials, with E.G. Kalnins, Journal of Computational
and Applied Mathematics, 68 (1996) 197-207. PDF Postscript
- Integrability, Stäckel spaces and rational
potentials, with
E.G. Kalnins and S. Benenti, J. Math. Phys., 38, (1997) 2345-2365. PostScript
- Superintegrability and associated polynomial solutions.
Euclidean space and the sphere in two dimensions, with E.G. Kalnins and
G.S. Pogosyan, J. Math. Phys., 37, 6439 (1996). PostScript
- Superintegrability on the two dimensional hyperboloid, with
E.G. Kalnins and G.S. Pogosyan, J. Math. Phys., 38, 5416--5433 (1997) PDF
- Tensor products of q-superalgebras and q-series
identities. I , with Won Sang Chung and E.G. Kalnins, in "Algebraic
Methods and $q$-Special Functions", Edited by: Jan Felipe van Diejen
and Luc Vinet, CRM Proceedings ; Lecture Notes, 22, American
Mathematical Society, 1999. Postscript
- The equivalence of SUQ(2) and a quantum deformation of SU(2)
in the cartesian basis, with Won Sang Chung and E.G.
Kalnins, submitted. PostScript
- Tensor products of q-superalgebra representations and q-series
identities, with Won Sang Chung and E.G. Kalnins, J. Physics A, 30,
7147--7166, (1997).PostScript
- Superintegrability on the two dimensional hyperboloid II, with
Ye. M. Hakobyan, E.G. Kalnins and G.S. Pogosyan, J. Math. Phys., 40,
2291--2306 (1999) PDF PostScript
- Superintegrability in two dimensional complex Euclidean space,
with E.G. Kalnins and G.S. Pogosyan, J.Math. Phys. (to appear). PostScript
- Superintegrability in three dimensional Euclidean space, with
E.G. Kalnins and G.S. Pogosyan, J. Math. Phys., 40, 708--725, (1999) PDF PostScript
- Contractions of Lie algebras and special function identities,
with E.G. Kalnins and G.S. Pogosyan, J. Phys. A 32,4709--4732, (1999) PDF PostScript
- Separability of wave equations, with E.G. Kalnins and G.C.
Williams, 33-51, in ``Black Holes, Gravitational Radiation and the
Universe, Essays in honor of C.V. Vishveshwara'', B.R. Iyer and B.
Bhawal, eds., Kluwer Academic Publishers, Dordrecht, 1999. PostScript
- Superintegrability and Special Functions in Mathematical
Physics, with E. G. Kalnins and G.S. Pogosyan, Proceedings of ``III
International Workshop on Classical and Quantum Integrable Systems",
Yerevan, Armenia, (June 29 --- July 04,1998), (to appear) PostScript
- Coulomb-oscillator duality in spaces of constant curvature,
with E. G. Kalnins and G. S. Pogosyan, J. Math. Phys. 41,
2629-2657, (2000) PDF Postscript
- The Coulomb-oscillator relation on N-dimensional
spheres and hyperboloids; with E. G. Kalnins and G. S. Pogosyan, Phys.
Atomic Nuclei 65 , no. 6, 1086--1094, (2002) PDF
- Completeness of multiseparable superintegrability in E(2,C),
with E.G. Kalnins and G.S. Pogosyan, J.Phys.A: Math Gen.
33,4105, (2000) PDF Postscript
- Completeness of multiseparable superintegrability on the complex
2-sphere, with E.G. Kalnins and G.S. Pogosyan, J. Physics A: Math. Gen.
33, 6791-6806, (2000) PDF Postscript
- Special functions and perturbations of black holes, with
E.G. Kalnins, G.F. Torres Del Castillo and G.C. Williams, in ``Special Functions (Hong Kong, 1999), Proceedings
of the International Workshop on Special Functions-Asymptotics,
Harmonic Analysis and Mathematical Physics (IWSF'99),'' C. Dunkl,
M. Ismail and R. Wong (Eds), World Scientific, 140-151. (2000) PDF PostScript
- Multiseparabilty and superintegrability for classical and
quantum systems, 129-156, in "Integrable Systems: From Classical to
Quantum". J. Harnad, G. Sabidussi and P. Winternitz,, eds., CRM
Proceedings and lecture Notes, Vol. 26, American Mathematical
Society, 2000 PDF Postscript
- Integrability and Stäckel spaces, with
E.G.Kalnins and S.
Benenti, in `` Symmetry methods in physics'', Vol. 1 (Dubna, 1995),
298--305, Joint Inst. Nuclear Res., Dubna, 1996.
- q-algebra and q-superalgebra tensor products and
identities for special functions, with E.G.Kalnins, VIII International
Conference on Symmetry Methods in Physics (Dubna, 1997). Phys. Atomic
Nuclei 61 ,
no. 10, 1659--1665, (1998) PostScript
- Completeness of multiseparable superintegrability in two
dimensions, with E.G. Kalnins and G.S. Pogosyan, International
Conference on Symmetry Methods in Physics (Dubna, 2000), Phys.
Atomic Nuclei 65 , no. 6, 1033--1035,
(2002) PostScript
- Completeness of superintegrability in two-dimensional constant
curvature spaces, with E.G. Kalnins, J. Kress and G.S. Pogosyan, J.
Phys. A: Math Gen. 34. 4705--4720, (2001) PDF PostScript
- On superintegrable symmetry breaking potentials in n-dimensional
Euclidean space, with E.G. Kalnins, G.C. Williams,and G.S.
Pogosyan, J. Phys. A: Math Gen. 35. 4655--4773, (2002) PDF PostScript
- Complete sets of invariants for dynamical systems that
admit a separation of variables, with E.G. Kalnins , J.M. Kress and
G.Pogosyan , J. Math. Phys. 43, 3592--3609, (2002) PDF PostScript
- Superintegrable systems in Darboux spaces, with E.G. Kalnins ,
J.M. Kress and P. Winternitz , J. Math. Phys. 44,
5811--5848, (2003) PDF PostScript
- Infinite order symmetries for two-dimensional separable
Schrödinger equations, with E.G. Kalnins and G.S.
Pogosyan, Proceedings of Institute of Mathematics, NAS of
Ukraine, 50, Part
I,184--195, (2004) PDF
- Infinite order symmetries for quantum separable systems,
with E.G. Kalnins, J.M. Kress and G.S. Pogosyan, International
Conference on Symmetry Methods in Physics (Yerevan,
2003) Phys.
Atomic Nuclei ,
68, num: 10, 1817-1824, 2005, PostScript
PDF
- Variable separation in mathematical physics: From intuitive
concept to mathematical tool, with E.G. Kalnins, Phil. Trans. R.
Soc. A. (to appear) PostScript
PDF
- The Cheshire Cat effect in Lie theory. Lamé and Heun
functions. In Proceedings Volume of the XXV International
Colloquium on Group Theoretical Methods in Physics, George S. Pogosyan,
Luis Edgar Vicent, and Kurt Bernardo Wolf, editors, Institute of
Physics/Canopus Press, Bristol UK, 2005 PostScript PDF
- Jacobi, ellipsoidal coordinates, and superintegrable systems,
with E.G. Kalnins and J.M. Kress, Journal of Nonlinear Mathematical
Physics, 12, no. 2, 209--229, (2005) PostScript PDF
- Second order superintegrable systems in conformally flat spaces.
1. 2D classical structure theory, with E.G. Kalnins and J.M. Kress , J.
Math. Phys., 46, 053509, (2005) PostScript
PDF
- Second order superintegrable systems in conformally flat spaces.
2. The classical 2D Stäckel transform, with E.G. Kalnins
and J.M.
Kress, J. Math. Phys., 46, 053510, (2005) PostScript
PDF
- Complete sets of invariants for classical systems, pp. 125-135,
in "Superintegrability in Classical and Quantum Systems". P. Tempesta
et al., eds., CRM Proceedings and Lecture Notes, Vol. 37,
American Mathematical Society, 2004
- Jacobi elliptic coordinates, functions of Heun and
Lamé type
and the Niven transform, with E.G. Kalnins, Random and Chaotic
Dynamics,
10, 487-508 (2005) PostScript PDF
- Second order superintegrable systems in conformally flat spaces.
3. 3D classical structure theory, with E.G. Kalnins and J.M.
Kress, J. Math. Phys., 46, 103507, (2005) PostScript
PDF
- Exact and quasi-exact solvability of second order superintegrable
quantum systems. I. Euclidean space preliminaries, with E.G. Kalnins
and G. S. Pogosyan, J. Math. Phys., 47, 033502, (2006) PostScript PDF
- Second order superintegrable systems in three dimensions, SIGMA,
Vol. 1 (2005), Paper 015, 17 pages. http://www.emis.de/journals/SIGMA/
PostScript
PDF
- Classification of superintegrable systems in three
dimensions, with E.G. Kalnins and J.M. Kress, in Quantum Theory and
Symmetries IV
ed. V.K. Dobrev, Heron Press, Sofia, (2006) PostScript PDF
- Second-order superintegrable quantum systems, with E.G. Kalnins
and J.M. Kress, Phys.
Atomic Nuclei 70 , no. 3, 576--583, (2007) PostScript
- Nondegenerate superintegrable systems in n-dimensional spaces of
constant curvature, with E.G. Kalnins and J.M. Kress,
Phys.
Atomic Nuclei 70 , no. 3, 545--553, (2007) PostScript
- Second order superintegrable systems in conformally flat spaces.
4. The classical 3D Stäckel transform and 3D
classification
theory, with E.G. Kalnins and J.M. Kress, J. Math. Phys., 47,
043514, (2006) PostScript
PDF
- Second order superintegrable systems in conformally flat spaces.
5. 2D and 3D quantum systems, with E.G. Kalnins and J.M.
Kress, J.
Math. Phys., 47, 093501 (2006) PostScript
PDF
- Exact and quasi-exact solvability of second order superintegrable
quantum systems. II. Connection with separation of variables, with E.G.
Kalnins and G. S. Pogosyan, J.
Math. Phys., 48, 023503 (2007) PostScript PDF
- Fine structure for second order superintegrable systems. with
E.G. Kalnins and J.M. Kress, in
IMA Volume 144: Symmetries and Overdetermined Systems of Partial Differential
Equations (Michael Eastwood and Willard Miller, Jr., Editors) Springer, New York, (2007) PostScript PDF
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Exact and quasi-exact solvability of second order superintegrable quantum systems, with E.G. Kalnins and G. S. Pogosyan, in IMA Volume 144: Symmetries and Overdetermined Systems of Partial Differential Equations (Michael Eastwood and Willard Miller, Jr., Editors), Springer, New York, (2007) PDF
- Nondegenerate 2D complex Euclidean superintegrable systems and
algebraic varieties, with E.G. Kalnins and J.M.
Kress, J. Phys. A: Math. Theor. 40, 3399-3411, (2007) PostScript
- Fine structure for 3D second order superintegrable systems:
3-parameter potentials, with E.G. Kalnins and J.M.
Kress, J. Phys. A: Math. Theor. 40, 5875-5892, (2007) PostScript
PDF
- Nondegenerate 3D complex Euclidean superintegrable systems and
algebraic varieties, with E.G. Kalnins and J.M.
Kress, J. Math. Phys. 48, 113518, 26 pages, (2007) PostScript
PDF
- Wilson polynomials and the generic superintegrable system on the
2-sphere, with E.G. Kalnins and S. Post, J. Phys. A: Math.
Theor. 40, 11525-11538, (2007) PostScript
PDF
- Quantum and classical models for quadratic algebras associated
with second order superintegrable systems, with E.G. Kalnins and S.
Post ,SIGMA 4, 008, 21 pages; arXiv:0801.2848,(2008)
PostScript PDF
- Models of quadratic quantum algebras and their relation to
classical superintegrable systems, with E. G. Kalnins and S. Post,
Physics of Atomic Nuclei, 72, no. 5, 801-808 (2009) PDF
- Models for the 3D singular isotropic oscillator quadratic
algebra, with E. G. Kalnins and S. Post,Physics of
Atomic Nuclei Volume 73, Number 2,
,
(2010) PDF
- Structure theory for second
order 2D superintegrable systems with 1-parameter potentials, with E.
G. Kalnins, J. M. Kress, and S.
Post. SIGMA 5 (2009), 008, 24 pages
arXiv:0901.3081
doi:10.3842/SIGMA.2009.008
PostScript
- Coupling constant metamorphosis and Nth order symmetries in
classical and quantum mechanics, with E. G. Kalnins and S. Post,
J. Phys. A: Math. Theor. 43 (2010) 035202. (20 pages) PDF Postscript doi: 10.1088/1751-8113/43/3/035202
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Laplace-type equations as conformal superintegrable systems, with E. G. Kalnins, J. M. Kress, and S. Post. Advances in Applied Mathematics 46 (2011) 396–416 Postscript , (older more expanded version: PDF PostScript)
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Families of classical subgroup separable superintegrable systems, with E. G. Kalnins, and J. M. Kress. J. Phys. A: Math. Theor. 43 (2010) 092001. PDF arXiv:0912.3158v1 [math-ph]
- Superintegrability and higher order constants for classical
and quantum systems, with E. G. Kalnins and G. S. Pogosyan,
arXiv:0912.2278v1
[math-ph] Physics of Atomic Nuclei, 74, No. 6, 914-918 (2011)
- Superintegrability and higher
order integrals for quantum systems, with E. G. Kalnins, and J. M. Kress. .
PDF
arXiv:1002.2665v1
[math-ph] J. Phys. A: Math. Theor. 43 (2010) 265205.
- Tools for verifying classical
and quantum superintegrability, with E. G. Kalnins, and J. M. Kress. .
PDF (with correction for system [s9],
arXiv:1006.0864v1
[math-ph]
http://www.emis.de/journals/SIGMA/2010/066/ SIGMA 6 (2010), 066, 23 pages
- Two-variable Wilson polynomials and the generic superintegrable system on the 3-sphere, with E. G. Kalnins, and S. Post. http://www.emis.de/journals/SIGMA/2011/051/
[math-ph] SIGMA 7 (2011), 051, 26 pages
- A recurrence relation approach to higher order quantum superintegrability, with E. G. Kalnins, and J. M. Kress. .
http://www.emis.de/journals/SIGMA/2011/031/
[math-ph] SIGMA 7 (2011), 031, 24 pages
- Structure results for higher order symmetry algebras of 2D classical
superintegrable systems, with E. G. Kalnins. .
arXiv:1011.5292
[math-ph] Journal of Nonlinear Systems and Applications (JNSA). 3, Number 1, 29-40, (2012)
- Structure theory for extended Kepler-Coulomb 3D classical
superintegrable systems, with E. G. Kalnins. .
arXiv:1202.0197
[math-ph] SIGMA 8 (2012), 034, 25 pages
- The Mathematics of Signal Processing, (a textbook of about 450 pages)
with Stephen Damelin,
Cambridge Texts in Applied Mathematics (No. 48), Cambridge University Press, 2012.
(ISBN-13: 9781107013223)
- Structure relations for the symmetry algebras of quantum
superintegrable systems, with E. G. Kalnins and J. M. Kress. .
J. Phys.: Conf. Ser. 343 012075 doi:10.1088/1742-6596/343/1/012075
(2012)
- Superintegrability in a non-conformally-flat space, with E. G. Kalnins and J. M. Kress. J. Phys. A: Math. Theor. 46 (2013) 022002
- Structure theory for extended Kepler-Coulomb 3D quantum superintegrable systems. PDF
Proceedings of the XXIX
International Colloquium on Group-Theoretical Methods in Physics World Scientific, Singapore, Vol. 11 in the “Nankai Series in Pure, Applied Mathematics and Theoretical Physics”; ISBN 978-981-4518-54-3 (2013) 223-228
- Solutions of Helmholtz and Schr\"odinger equations with a side condition and nonregular separation of variables, with P. Broadbridge and C. Chanu. SIGMA 8 (2012), 089, 31 pages (2012)
- Extended Kepler-Coulomb quantum superintegrable systems in 3 dimensions, with E. G. Kalnins and J. M. Kress. PDF
J. Phys. A: Math. Theor. 46 (2013) 085206.
- Contractions of 2D 2nd order quantum superintegrable systems and the Askey scheme for hypergeometric orthogonal polynomials, with E. G. Kalnins and S. Post. PDF and postscript
SIGMA 9 (2013), 057, 28 pages
- Classical and Quantum Superintegrability with Applications , with S. Post and P. Winternitz. PDF/PS PDF
J. Phys. A: Math. Theor. 46 (2013) 423001. (a 97 page topical review paper)
- The theory of contractions of 2D 2nd order quantum superintegrable
systems and its relation to the Askey scheme for hypergeometric orthogonal
polynomials http://arxiv.org/abs/1310.2202 2014 J. Phys.: Conf. Ser. 512 012012
(http://iopscience.iop.org/1742-6596/512/1/012012)
- Quadratic algebra contractions and 2nd order superintegrable systems, with E. G. Kalnins http://arxiv.org/abs/1401.0830 Analysis and Application 12, 583-612, DOI: 10.1142/S0219530514500377 2014
- Particle in a field of two centers in prolate spheroidal coordinates:
integrability and solvability, with A. Turbiner PDF J. Phys. A: Math. Theor. (Fast Track Publication), 47 (2014) 192002 (10pp) doi:10.1088/1751-8113/47/19/19200
- (Quasi)-exact-solvability on the sphere S^n, with A. Turbiner PDF J. Math. Phys. 56, 023501 (2015); http://dx.doi.org/10.1063/1.4906909
- Wilson polynomials/functions and intertwining operators for the generic quantum superintegrable system on the 2-sphere, with Q. Li PDF 2015 J. Phys.: Conf. Ser. 597 012059
(http://iopscience.iop.org/1742-6596/597/1/012059)
- A Geometrical Perspective on the Coherent Multimode Optical Field and Mode-Coupling Equations, with William A. Wood and Michal Mlejnek PDF IEEE Journal of Quantum Electronics, 51, No 7, 6100206, July, 2015
- Structure Relations and Darboux Contractions
for 2D 2nd Order Superintegrable Systems, with Robin Heinonen, Ernest G. Kalnins, and Eyal Subag PDF SIGMA 11 (2015), 043, 33 pages
- Laplace equations, conformal superintegrability and B\^ocher
contractions,
Authors: E. Kalnins, W. Miller Jr, and E. Subag PDF Acta Polytechnica 56, 3, 214-223, (2016)
- Examples of complete solvability of 2D classical superintegrable systems,
Authors: Willard Miller Jr., Qiushi Li, Yuxuan Chen, Ernie G. Kalnins PDF SIGMA 11 (2015), 088, 51 pages
- B\^ocher contractions of conformally superintegrable Laplace equations,
Authors: Ernie G. Kalnins, Willard Miller Jr., Eyal Subag PDF   SIGMA 12 (2016), 038, 31 pages;
B\^ocher contractions of conformally superintegrable Laplace equations: Detailed computations,
Authors: Ernie G. Kalnins, Willard Miller Jr., Eyal Subag PDF
- Conformal Laplace superintegrable systems in 2D: Polynomial invariant
subspaces,
Authors: M.A. Escobar-Ruiz and Willard Miller Jr PDF J. Phys. A: Math. Theor. 49 305202, (2016).
- Separation equations for 2D superintegrable systems on constant
curvature spaces,
Authors: M.A. Escobar-Ruiz, E. G. Kalnins and Willard Miller Jr PDF, J. Phys. A: Math. Theor. 50, 385202, 2017.
- B\^ocher and abstract contractions of 2nd order quadratic algebras,
Authors: M. A. Escobar Ruiz, E. G. Kalnins, W. Miller, Jr. and E. Subag PDF SIGMA 13 (2017) 013 38 pages.
- Toward a classification of semidegenerate 3D superintegrable systems,
Authors: M. A. Escobar Ruiz and W. Miller, Jr. PDF J. Phys. A: Mathematical and Theoretical, 50 095203 (2017).
- Three-body problem in 3D space: ground state, (quasi)-exact-solvability,
Authors: Alexander V Turbiner, W. Miller, Jr, and M. A. Escobar Ruiz. PDF J. Phys. A: Math. Theor. 50 215201 (2017).
- Three-body problem in d-dimensional space: ground state, (quasi)-exact-solvability,
Authors: Alexander V Turbiner, W. Miller, Jr, and M. A. Escobar Ruiz. PDF Journal of Mathematical Physics 59, 022108 (2018); https://doi.org/10.1063/1.4994397.
- Contractions of degenerate quadratic algebras, abstract and geometric,
Authors: M.A. Escobar Ruiz, W. Miller Jr. and E. Subag PDF SIGMA 13 (2017), 099, 32 pages.
- The quantum n-body problem in dimension d\ge n-1: ground state,
Authors: W. Miller, Jr, Alexander V Turbiner, and M. A. Escobar Ruiz.
PDF 2018 J. Phys. A: Math. Theor. 51 205201
- Separation of variables and Superintegrability:
The symmetry of solvable systems, Authors: E. G. Kalnins, J. M. Kress, and W. Miller, Jr.
Instititute of Physics, UK, 2018, ISBN: 978-0-7503-1314-8,
e-book (2018).
- Four-body problem
in d-dimensional space: ground state, (quasi)-exact-solvability. IV,
Authors: M. A. Escobar Ruiz, W. Miller, Jr, and Alexander V Turbiner,
PDF Journal of Mathematical Physics 60, 062101 https://doi.org/10.1063/1.5083129 (2019).
- A new approach to analysis of 2D higher order quantum superintegrable
systems,
Authors: Bjorn K. Berntson, Ian Marquette and Willard Miller Jr,
PDF proceedings volume ebook, M. B. Paranjape et al. (eds.),Quantum Theory and Symmetries, CRM Series in Mathematical Physics,https://doi.org/10.1007/978-3-030-55777-5_10,
pages 111-120, (2021).
- Three-body closed chain of interactive (an)harmonic oscillators and
the
algebra sl(4)
Authors: Alexander V Turbiner, W. Miller, Jr. and M. A. Escobar Ruiz
PDF J. Phys. A: Math. Theor. 53 055302 (2019))
- Superintegrable three-body problems
Authors: Alexander V Turbiner, W. Miller, Jr. and M. A. Escobar Ruiz
PDF (submitted) (2019).
- Classification of Calogero-like 2nd order superintegrable systems in 3
dimensions, Authors: B.K. Berntson, E.G. Kalnins and W. Miller, J.
PDF SIGMA 16 (2020), 135, 33 pages.
- Nonexistence of Calogero-like 2nd order superintegrable systems of class O(4) on the complex 3-sphere Authors: B.K. Berntson, E.G. Kalnins and W. Miller, J.
PDF (2020).
-
A new way to classify 2D higher order quantum superintegrable systems
Authors: Bjorn K. Berntson, Ian Marquette and Willard Miller Jr,
PDF Journal of Physics A: Mathematical and Theoretical, 53 (49) 494003, 1-21. doi: 10.1088/1751-8121/abc04a (2020).
-
Classical $n$-body system in geometrical and volume variables. I.
Three-body case
Authors: A. M. Escobar-Ruiz, R. Linares, Alexander V Turbiner and Willard Miller Jr,
PDF (2021).
International Journal of Modern Physics A
Vol. 36, No. 18 (2021) 2150140 (26 pages)
-
From two-dimensional (super-integrable) quantum dynamics to (super-integrable) three-body dynamics
Authors: A. M. Escobar-Ruiz, R. Linares, Alexander V Turbiner and Willard Miller Jr,
PDF J. Phys. A: Math. Theor. 54 015204 (2021).
-
Four-body (an)harmonic oscillator in d-dimensional space: S-states, (quasi)-exact-solvability, hidden algebra sl(7)
Authors: A. M. Escobar-Ruiz, Alexander V Turbiner and Willard Miller Jr,
PDF
Journal of Mathematical Physics 62, 072103 (2021)