Codes and Expansions (CodEx) Seminar

Jakob Lemvig (Technical University of Denmark - DTU):
The Gabor frame set problem for Hermite functions

Frame set problems in Gabor analysis ask the question for which sampling and modulation rates the corresponding time-frequency shifts of a generating window allow for stable reproducing formulas of \(L^2\)-functions. In this talk we consider frame sets for Hermite functions, and we show how certain modular characteristics of the Zak transform of Hermite functions play an important role in these frame set problems. From both numerical results in Python and theoretical result we will see that the frame sets of Hermite functions of order two or larger must have a rather complicated structure, in particular, we will show that the so-called frame set conjecture of Hermite functions is false for all orders larger than or equal to two.