pp-adic refinable functions and MRA-based wavelets

The main goal of this paper is the development of the MRA theory in L2(Qp)L2(Qp). We described a wide class of pp-adic refinement equations generating pp-adic multiresolution analyses. A method for the construction of pp-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 pp-adic Haar bases which were known before.