English

$p$-Adic multiresolution analyses

Functional Analysis 2008-10-08 v1 Number Theory

Abstract

We study pp-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 pp-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

R2 v1 2026-06-21T11:28:03.815Z