Problems in time-frequency analysis
Faculty of Mathematics, University of Vienna
given at esi18 (18.03.19)
Time-frequency analysis, i.e., the mathematics of time-frequency shifts (or phase-space shifts), is full of open problems that seem to require the input from other fields. This survey will present and discuss some challenges.
(a) What is the nature of the zero set of the short-time Fourier transform or of the Wigner distribution? With connections to complex analysis.
(b) For which windows can one describe all lattices that generate a Gabor frame? With connections to complex analysis and approximation theory.
(c) What is the precise behavior of the frame bounds of a Gabor frame with Gaussian window over a lattice? With connections to complex analysis, theta functions, and tiling and packing problems.