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p-Adic Multiresolution Analysis and Wavelet Frames

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Abstract

We study p-adic multiresolution analyses (MRAs). A complete characterization of test functions generating an MRA (scaling functions) is given. We prove that only 1-periodic test functions may be taken as orthogonal scaling functions and that all such scaling functions generate the Haar MRA. We also suggest a method for constructing sets of wavelet functions and prove that any set of wavelet functions generates a p-adic wavelet frame.

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Authors and Affiliations

  1. Interdisziplinres Zentrum für Komplexe Systeme, Universität Bonn, Römerstraße 164, 53117, Bonn, Germany

    S. Albeverio

  2. St.-Petersburg Department of Steklov Institute of Mathematics, Fontanka-27, 191023, St. Petersburg, Russia

    S. Evdokimov

  3. Department of Applied Mathematics and Control Processes, St. Petersburg State University, Universitetskii pr.-35, Petrodvorets, 198504, St. Petersburg, Russia

    M. Skopina

Authors
  1. S. Albeverio
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  2. S. Evdokimov
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  3. M. Skopina
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Corresponding author

Correspondence to M. Skopina.

Additional information

Communicated by Hans G. Feichtinger.

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Albeverio, S., Evdokimov, S. & Skopina, M. p-Adic Multiresolution Analysis and Wavelet Frames. J Fourier Anal Appl 16, 693–714 (2010). https://doi.org/10.1007/s00041-009-9118-5

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  • DOI: https://doi.org/10.1007/s00041-009-9118-5

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