Invertibility of the Gabor frame operator on the Wiener amalgam space

Krishtal, Ilya A.; Okoudjou, Kasso A.

Invertibility of the Gabor frame operator on the Wiener amalgam space

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Description

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 $W(L^{\infty}, \ell^{1}_ν)(\mathbb{R}^{d})$, 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}_ν)(\mathbb{R}^{d}) $