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Operators commuting with a discrete subgroup of translations

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Abstract

We study the structure of operators from the Schwartz space S(ℝn) into the tempered distributions S′(ℝn) that commute with a discrete subgroup of translations. The formalism leads to simple derivations of recent results about the frame operator of shift-invariant systems, Gabor, and wavelet frames.

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Authors and Affiliations

  1. Faculty of Mathematics, University of Vienna, Nordbergstraße 15, 1090, Vienna, Austria

    H. G. Feichtinger & N. Kaiblinger

  2. Institute of Biomathematics and Biometry, GSF Research Center for Environment and Health, Ingolstädter Straße 1, D-85764, Neuherberg, Germany

    H. Führ & K. Gröchenig

Authors
  1. H. G. Feichtinger
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  2. H. Führ
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  3. K. Gröchenig
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  4. N. Kaiblinger
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Correspondence to H. G. Feichtinger.

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Communicated by Yoram Sagher

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Feichtinger, H.G., Führ, H., Gröchenig, K. et al. Operators commuting with a discrete subgroup of translations. J Geom Anal 16, 53–67 (2006). https://doi.org/10.1007/BF02930987

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  • DOI: https://doi.org/10.1007/BF02930987

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