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Gabor frames without inequalities

Karlheinz Gröchenig
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Abstract

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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Karlheinz Gröchenig. 2007-03-13. Gabor frames without inequalities. https://arxiv.org/abs/math/0703379

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