Gabor frames without inequalities

Details Gabor frames without inequalities Gabor frames without inequalities

2007-03-13

arxiv.org/abs/math/0703379v1

International Mathematics Research Notices 2007 (2007), rnm111-21

Mathematics

Functional Analysis

16 pages

Scientific paper

We prove fourteen equivalent conditions for a set of timefrequency shifts on
a lattice to be a frame for L^2. Remarkably, several of these conditions can be
formulated without an inequality. In particular, instead of checking the
invertibility of the frame operator on L^2 it suffices to verify that it is
one-to-one on a certain subspace of tempered distributions.

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