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Gabor pairs, and a discrete approach to wave-front sets

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Abstract

We introduce admissible lattices and Gabor pairs to define discrete versions of wave-front sets with respect to Fourier–Lebesgue and modulation spaces. We prove that these wave-front sets agree with each other and with corresponding wave-front sets of “continuous type”. This implies that the coefficients of a Gabor frame expansion of f are parameter dependent, and describe the wave-front set of f.

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Authors and Affiliations

  1. Department of Computer Science, Physics and Mathematics, Linnæus University, Växjö, Sweden

    Karoline Johansson & Joachim Toft

  2. Department of Mathematics and Informatics, University of Novi Sad, Novi Sad, Serbia

    Stevan Pilipović & Nenad Teofanov

Authors
  1. Karoline Johansson
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  2. Stevan Pilipović
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  3. Nenad Teofanov
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  4. Joachim Toft
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Corresponding author

Correspondence to Joachim Toft.

Additional information

Communicated by Karlheinz Gröchenig.

This research is supported by MNTR of Serbia, project no 174024.

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Johansson, K., Pilipović, S., Teofanov, N. et al. Gabor pairs, and a discrete approach to wave-front sets. Monatsh Math 166, 181–199 (2012). https://doi.org/10.1007/s00605-011-0288-2

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  • DOI: https://doi.org/10.1007/s00605-011-0288-2

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