English

Gabor frames without inequalities

Functional Analysis 2011-04-27 v1 Operator Algebras

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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Cite

@article{arxiv.math/0703379,
  title  = {Gabor frames without inequalities},
  author = {Karlheinz Gröchenig},
  journal= {arXiv preprint arXiv:math/0703379},
  year   = {2011}
}

Comments

16 pages