p-Adic Haar Multiresolution Analysis and Pseudo-Differential Operators

NON-HAAR p-ADIC WAVELETS AND THEIR APPLICATION TO PSEUDO-DIFFERENTIAL OPERATORS AND EQUATIONS

In this paper a countable family of new compactly supported non-Haar p-adic wavelet bases in L(Q p ) is constructed. We use the wavelet bases in the following applications: in the theory of p-adic pseudo-differential operators and equations. Namely, we study the connections between wavelet analysis and spectral analysis of p-adic pseudo-differential operators. A criterion for a multidimensional...

FUNDAMENTAL SOLUTIONS OF PSEUDO-DIFFERENTIAL OPERATORS OVER p−ADIC FIELDS

We show the existence of fundamental solutions for p−adic pseudodifferential operators with polynomial symbols.

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...

Haar wavelets and multiresolution analysis

Automorphic Pseudo-differential Operators

For recent developments of this work in the classical direction, especially to generalizing to modular groups acting on higher dimensional spaces, see papers of Min Ho Lee: http://www.math.uni.edu/ lee/pub.html. He has, for example, developed the Hilbert modular case. Also, Olav Richter’s work on Rankin-Cohen brackets: http://www.math.unt.edu/ richter/. Work of Conley on 1/2-integral weight: ht...