p-Adic refinable functions and MRA-based wavelets

Abstract

We described a wide class of $p$-adic refinable equations generating $p$-adic multiresolution analysis. A method for the construction of $p$-adic orthogonal wavelet bases within the framework of the MRA theory is suggested. A realization of this method is illustrated by an example, which gives a new 3-adic wavelet basis. Another realization leads to the $p$-adic Haar bases which were known before.