Related papers: Non-Haar $p$-adic wavelets and their application t…
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…
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.
Wavelet analysis has been extended to the $p$-adic line $\mathbb{Q}_p$. The $p$-adic wavelets are complex valued functions with compact support. As in the case of real wavelets, the construction of the basis functions is recursive,…
New orthonormal basis of eigenfunctions for the Vladimirov operator of p-adic fractional derivation is constructed. The map of p-adic numbers onto real numbers (p-adic change of variables) is considered. This map (for p=2) provides an…
The approach to p-adic wavelet theory from the point of view of representation theory is discussed. p-Adic wavelet frames can be constructed as orbits of some p-adic groups of transformations. These groups are automorphisms of the tree of…
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…
A variety of different orthogonal wavelet bases has been found in L_2(R) for the last three decades. It appeared that similar constructions also exist for functions defined on some other algebraic structures, such as the Cantor and Vilenkin…
A family of orthonormal bases, the ultrametric wavelet bases, is introduced in quadratically integrable complex valued functions spaces for a wide family of ultrametric spaces. A general family of pseudodifferential operators, acting on…
We construct new bases of real functions from $L^{2}\left(B_{r}\right)$ and from $L^{2}\left(\mathbb{Q}_{p}\right)$. These functions are eigenfunctions of the $p$-adic pseudo-differential Vladimirov operator, which is defined on a compact…
This paper is devoted to wavelet analysis on adele ring $\bA$ and the theory of pseudo-differential operators. We develop the technique which gives the possibility to generalize finite-dimensional results of wavelet analysis to the case of…
Pseudo-differential operator equations with parameter are studied. Uniform separability properties and resolvent estimates are obtained in terms of fractional derivatives. Moreover, maximal regularity properties of the pseudo-differential…
We show that translations and dilations of a p-adic wavelet coincides (up to the multiplication by some root of one) with a vector from the known basis of discrete p-adic wavelets. In this sense the continuous p-adic wavelet transform…
We define a family of pseudodifferential operators on the Hilbert space $L^2(\mathbf{Q}_p)$ of complex valued square-integrable functions on the $p$-adic number field $\mathbf{Q}_p$. The Riemann zeta-function and the related Dirichlet…
In this article, we study a large class of radial probability density functions defined on the p-adic numbers from which it is possible to obtain certain non-archimedean pseudo-differential operators. These operators are associated with…
We discuss transformation of p-adic pseudodifferential operators (in the one-dimensional and multidimensional cases) with respect to p-adic maps which correspond to automorphisms of the tree of balls in the corresponding p-adic spaces. In…
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…
We define and study pseudo-differential operators on a class of fractals that include the post-critically finite self-similar sets and Sierpinski carpets. Using the sub-Gaussian estimates of the heat operator we prove that our operators…
Time series defined by a p-adic pseudo-differential equation is investigated using the expansion of the time series over p-adic wavelets. Quadratic correlation function is computed. This correlation function shows a degree--like behavior…
A family of orthonormal bases of ultrametric wavelets in the space of quadratically integrable with respect to arbitrary measure functions on general (up to some topological restrictions) ultrametric space is introduced. Pseudodifferential…
The goal of this paper is to study certain p-adic differential operators on automorphic forms on U(n,n). These operators are a generalization to the higher-dimensional, vector-valued situation of the p-adic differential operators…