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Gabor Frames without Inequalities

by: Karlheinz Gröchenig
International Mathematics Research Notices, Vol. 2007 (1 January 2007), doi:10.1093/imrn/rnm111  Key: citeulike:11546127

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Abstract

We study the frame property of sets of time-frequency shifts (Gabor frames) on a lattice and prove that thirteen conditions are equivalent to it. Remarkably, several of these conditions can be formulated without an inequality. In particular, instead of checking the invertibility of the frame operator on the Hilbert space L2(ℝd), it suffices to verify that it is one-to-one on a certain subspace of tempered distributions.


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