$p$-Adic multiresolution analyses

Details $p$-Adic multiresolution analyses $p$-Adic multiresolution analyses

2008-10-07

arxiv.org/abs/0810.1147v1

Mathematics

Functional Analysis

17 pages

Scientific paper

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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