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arXiv · 0802.1079

$p$-Adic multiresolution analysis and wavelet frames

S. Albeverio·S. Evdokimov·M. Skopina
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Abstract

We study $p$-adic multiresolution analyses (MRAs). A complete characterisation of test functions generating MRAs (scaling functions) is given. We prove that only 1-periodic test functions may be taken as orthogonal scaling functions. We also suggest a method for the construction of wavelet functions and prove that any wavelet function generates a $p$-adic wavelet frame.

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S. Albeverio, S. Evdokimov, M. Skopina. 2008-02-08. $p$-Adic multiresolution analysis and wavelet frames. https://arxiv.org/abs/0802.1079

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