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math.FA2026
Schwartz-Class Gabor Windows and the Balian-Low Classification
Andrei Caragea, Götz Pfander
A lattice Gabor frame consists of a window function and its time-frequency shifts along a lattice. We classify the lattices that admit Schwartz-class and, equivalently, Feichtinger…
math.FA2026
Tilings, packings, and the existence of Schwartz-class Gabor windows
Andrei Caragea, Mihail N. Kolountzakis, Götz Pfander
The existence and construction of Schwartz-class windows for lattice Gabor frames is a central problem in time--frequency analysis. For general time--frequency lattices, we charact…