中科院数学与系统科学研究院
数学研究所
学术报告
多复变与复几何研讨班
报告人：王煦 副教授 (挪威科技大学)
题 目：Kähler geometry methods in Gaussian Gabor frame theory
时 间：2023.09.07（星期四）15:00-17:00
地 点：zoom : 82643282555 密码：202308
https://zoom.us/j/82643282555?pwd=R05ZRkdKNUp0UFlMaWg0Z0RjcjBhQT09
摘 要： We investigate the frame set of regular multivariate Gaussian Gabor frames using methods from Kähler geometry such as Hörmander's $\dbar$-L2 estimate with singular weight, Demailly's Calabi--Yau method for Kähler currents and a Kähler-variant generalization of the symplectic embedding theorem of McDuff--Polterovich for ellipsoids. Our approach is based on the well-known link between sets of interpolation for the Bargmann-Fock space and the frame set of multivariate Gaussian Gabor frames. We state sufficient conditions in terms of a certain extremal type Seshadri constant of the complex torus associated to a lattice to be a set of interpolation for the Bargmann-Fock space, and give also a condition in terms of the generalized Buser-Sarnak invariant of the lattice. In particular, we obtain an effective Gaussian Gabor frame criterion in terms of the covolume for almost all lattices, which is the first general covolume criterion in multivariate Gaussian Gabor frame theory.
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