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p-Adic Multiresolution Analysis and Wavelet Frames |
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| Authors: | S. Albeverio S. Evdokimov M. Skopina |
| Affiliation: | 1. Interdisziplinres Zentrum für Komplexe Systeme, Universit?t Bonn, R?merstra?e 164, 53117, Bonn, Germany 2. St.-Petersburg Department of Steklov Institute of Mathematics, Fontanka-27, 191023, St. Petersburg, Russia 3. Department of Applied Mathematics and Control Processes, St. Petersburg State University, Universitetskii pr.-35, Petrodvorets, 198504, St. Petersburg, Russia |
| 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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