English

$p$-Adic multiresolution analysis and wavelet frames

Classical Analysis and ODEs 2008-02-11 v1

Abstract

We study pp-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 pp-adic wavelet frame.

Keywords

Cite

@article{arxiv.0802.1079,
  title  = {$p$-Adic multiresolution analysis and wavelet frames},
  author = {S. Albeverio and S. Evdokimov and M. Skopina},
  journal= {arXiv preprint arXiv:0802.1079},
  year   = {2008}
}

Comments

16 pages

R2 v1 2026-06-21T10:10:41.515Z