# Paley-Wiener theorem

Thursday, November 15, 2018 - 9:30am - 10:30am

Eric Opdam (Universiteit van Amsterdam)

Let omega be a rational n-form on C^n whose singular locus is a finite affine real hyperplane arrangement, and let b denote a base point in R^n outside the singular locus. Given a Paley-Wiener function f on C^n we define I_b(f) as the integral of f times omega over b+iR^n. By Cauchy’s theorem this linear functional I_b on the space PW(C^n) of Paley-Wiener functions only depends on the connected component of the complement of the singular locus of omega in which b lies.