periodic differential operator

Wednesday, April 26, 2017 - 10:30am - 11:30am
Braxton Osting (The University of Utah)
The spectrum of a Schroedinger operator with periodic potential generally consists of bands and gaps. In this talk, for fixed m, I'll consider the problem of maximizing the gap-to-midgap ratio for the m-th spectral gap over the class of potentials which have fixed periodicity and are pointwise bounded above and below. We prove that the potential maximizing the m-th gap-to-midgap ratio exists.
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