English

Haar bases for $L^2(\mathbb{Q}_2^2)$ generated by one wavelet function

Functional Analysis 2010-08-03 v1

Abstract

The concept of pp-adic quincunx Haar MRA was introduced and studied in~\cite{KS10}. In contrast to the real setting, infinitely many different wavelet bases are generated by a pp-adic MRA. We give an explicit description for all wavelet functions corresponding to the quincunx Haar MRA. Each one generates an orthogonal basis, one of them was presented in~\cite{KS10}. A connection between quincunx Haar bases and two-dimensional separable Haar MRA is also found.

Cite

@article{arxiv.1008.0163,
  title  = {Haar bases for $L^2(\mathbb{Q}_2^2)$ generated by one wavelet function},
  author = {S. Albeverio and M. Skopina},
  journal= {arXiv preprint arXiv:1008.0163},
  year   = {2010}
}

Comments

19 pages

R2 v1 2026-06-21T15:55:38.772Z