p-Adic multiresolution analysis and wavelet frames

2008/02/08 by Albeverio, S., Evdokimov, S., Skopina, M. · 1 citation
#11F85 #42C40 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.0802.1079

Abstract

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.

Cited by

• Wavelet Coorbit Spaces over Local Fields

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• p-Adic multiresolution analyses
• p-Adic refinable functions and MRA-based wavelets
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