$p$-Adic multiresolution analysis and wavelet frames

Details $p$-Adic multiresolution analysis and wavelet frames $p$-Adic multiresolution analysis and wavelet frames

2008-02-08

arxiv.org/abs/0802.1079v1

Mathematics

Classical Analysis and ODEs

16 pages

Scientific paper

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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