$p$-Adic multiresolution analyses

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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.
17 pages

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Functional Analysis, Number Theory

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http://salesiana.dossiersoluciones.com/handle/123456789/170870

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0810.1147
 http://arxiv.org/abs/0810.1147

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arXiv