Invertibility of the Gabor frame operator on the Wiener amalgam space

Details Invertibility of the Gabor frame operator on the Wiener amalgam space Invertibility of the Gabor frame operator on the Wiener amalgam space

2007-05-09

arxiv.org/abs/0705.1335v1

Mathematics

Functional Analysis

Scientific paper

We use a generalization of Wiener's $1/f$ theorem to prove that for a Gabor frame with the generator in the Wiener amalgam space $W(L^{\infty}, \ell^{1}_{\nu})(\mathbb{R}^{d})$, the corresponding frame operator is invertible on this space. Therefore, for such a Gabor frame, the generator of the canonical dual belongs also to $W(L^{\infty}, \ell^{1}_{\nu})(\mathbb{R}^{d}) $

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