title: Gabor frame sets of invariance: a Hamiltonian approach to Gabor frame deformations.
abstract: In this work we study families of pairs of window functions and lattices which lead to Gabor frames which all possess the same frame bounds. To be more precise, for every generalized Gaussiang, we will construct an uncountable family of lattices [Formula: see text] such that each pairing ofgwith some [Formula: see text] yields a Gabor frame, and all pairings yield the same frame bounds. On the other hand, for each lattice we will find a countable family of generalized Gaussians [Formula: see text] such that each pairing leaves the frame bounds invariant. Therefore, we are tempted to speak aboutGabor Frame Sets of Invariance.
authors: NuHAG, Faculty of Mathematics, University of Vienna, Oskar-Morgenstern-Platz 1, 1090 Vienna, Austria.
authors: Markus
authors: M
authors: Faulhuber
keywords: Frame bounds; Gabor frame; Hamiltonian deformation