p-ADIC WAVELETS

Se p 20 03 p – Adic pseudodifferential operators and p – adic wavelets

We introduce a new wide class of p–adic pseudodifferential operators. We show that the basis of p–adic wavelets is the basis of eigenvectors for the introduced operators.

Multidimensional basis of p - adic wavelets and representation theory

A multidimensional basis of p-adic wavelets is constructed. The relation of the constructed basis to a system of coherent states (i.e. orbit of action) for some p-adic group of linear transformations is discussed. We show that the set of products of the vectors from the constructed basis and p-roots of one is the orbit of the corresponding p-adic group of linear transformations.

p-adic refinable functions and MRA-based wavelets

p-adic Shearlets

The field $Q_{p}$ of $p$-adic numbers is defined as the completion of the field of the rational numbers $Q$ with respect to the  $p$-adic norm $|.|_{p}$. In this paper, we study the continuous and discrete $p-$adic shearlet systems on $L^{2}(Q_{p}^{2})$. We also suggest discrete $p-$adic shearlet frames. Several examples are provided.

ec 2 00 6 p - ADIC MULTIDIMENSIONAL WAVELETS AND THEIR APPLICATION TO p - ADIC PSEUDO - DIFFERENTIAL OPERATORS

In this paper we study some problems related with the theory of multidimensional p-adic wavelets in connection with the theory of multidimensional p-adic pseudo-differential operators (in the p-adic Lizorkin space). We introduce a new class of n-dimensional p-adic compactly supported wavelets. In one-dimensional case this class includes the Kozyrev p-adic wavelets. These wavelets (and their Fou...