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Pseudo-differential operators and existence of Gabor frames

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Abstract

We study from a pseudo-differential point of view the frame operator associated with a Gabor system. In particular we show how an application of the classical boundedness theorem of Calderón–Vaillancourt yields sufficient conditions for a Gabor system to form a frame in \(L^2\left( {\mathbb {R}}^d\right) \).

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Authors and Affiliations

  1. Dipartimento di Matematica, Università di Torino, Via Carlo Alberto 10, 10123, Torino, Italy

    Paolo Boggiatto & Gianluca Garello

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  1. Paolo Boggiatto
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  2. Gianluca Garello
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Correspondence to Gianluca Garello.

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Boggiatto, P., Garello, G. Pseudo-differential operators and existence of Gabor frames. J. Pseudo-Differ. Oper. Appl. 11, 93–117 (2020). https://doi.org/10.1007/s11868-019-00279-1

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  • DOI: https://doi.org/10.1007/s11868-019-00279-1

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