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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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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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Keywords

  • Gabor frames
  • Pseudo-differential operators
  • Calderón–Vaillancourt theorem

Mathematics Subject Classification

  • Primary 42C15
  • Secondary 42C40
  • 47G30
  • 35S05