$p$-Adic multiresolution analyses
Functional Analysis
2008-10-08 v1 Number Theory
Abstract
We study -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 -adic wavelet frame.
Cite
@article{arxiv.0810.1147,
title = {$p$-Adic multiresolution analyses},
author = {S. Albeverio and S. Evdokimov and M. Skopina},
journal= {arXiv preprint arXiv:0810.1147},
year = {2008}
}
Comments
17 pages