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arXiv · 0810.1147

$p$-Adic multiresolution analyses

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 a 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 Haar MRA. We also suggest a method of constructing sets of wavelet functions and prove that any set of wavelet functions generates a $p$-adic wavelet frame.

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S. Albeverio, S. Evdokimov, M. Skopina. 2008-10-07. $p$-Adic multiresolution analyses. https://arxiv.org/abs/0810.1147

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