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

Abstract

The concept of $p$-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 $p$-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.

19 pages

References in corpus (2)

• p-Adic refinable functions and MRA-based wavelets
• $p$-Adic multiresolution analysis and wavelet frames