Invertibility of the Gabor frame operator on the Wiener amalgam space

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Invertibility of the Gabor frame operator on the Wiener amalgam space

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∞, ` )(R), 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∞, ` )(R).

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ژورنال

عنوان ژورنال: Journal of Approximation Theory

سال: 2008

ISSN: 0021-9045

DOI: 10.1016/j.jat.2008.03.004