$p$-Adic multiresolution analysis and wavelet frames

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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.
16 pages

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Classical Analysis and ODEs, 42C40; 11F85

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http://salesiana.dossiersoluciones.com/handle/123456789/154425

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0802.1079
 http://arxiv.org/abs/0802.1079

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arXiv