Related papers: p-Adic refinable functions and MRA-based wavelets

In this paper, we construct a digraph structure on $p$-adic dynamical systems defined by rational functions. We study the conditions under which the functions are measure-preserving, invertible and isometric, ergodic, and minimal on…

We study the explicit construction of the Haar measure on the compact $p$-adic rotation group $\textrm{SO}(3)_p$ by nautical (Cardano) parametrization. Exploiting its topological group isomorphism with…

We propose a simple method to construct step mask and corresponding step wavelet functions that generate tight wavelet frames on the field of p-adic numbers. To construct tight wavelet frames we do not use the principle of unitary…

This note studies, and partially solves, 3 elementary questions about continuous rational functions on real (and p-adic) algebraic varieties: Can one restrict such a function to a subvariety? Can one extend such a function from a…

For an arbitrary matrix dilation, any integer n and any integer/semi-integer c, we describe all masks that are symmetric with respect to the point c and have sum rule of order n. For each such mask, we give explicit formulas for wavelet…

Spectral representations of the dilation and translation operators on $L^2({\mathbb R})$ are built through appropriate bases. Orthonormal wavelets and multiresolution analysis are then described in terms of rigid operator-valued functions…

A generalisation of the Shannon complex wavelet is introduced, which is related to raised cosine filters. This approach is used to derive a new family of orthogonal complex wavelets based on the Nyquist criterion for Intersymbolic…

We define refined invariants which "count" nodal curves in sufficiently ample linear systems on surfaces, conjecture that their generating function is multiplicative, and conjecture explicit formulas in the case of K3 and abelian surfaces.…

The theory of (Muckenhoupt) weights arises in many areas of analysis, for example in connection with bounds for singular integrals and maximal functions on weighted spaces. We prove that a certain averaging process gives a method for…

The detail structure of the wave function is analyzed at various refinement levels using the methods of wavelet analysis. The eigenvalue problem of a model system is solved in granular Hilbert spaces, and the trajectory of the eigenstates…

We give a new class of multidimensional $p$-adic continued fraction algorithms. We propose an algorithm in the class for which we can expect that multidimensional $p$-adic version of Lagrange's Theorem holds.

Multifractal analysis has become a standard signal processing tool,for which a promising new formulation, the p-leader multifractal formalism, has recently been proposed. It relies on novel multiscale quantities, the p-leaders, defined as…

In order to have a multiresolution analysis, the scaling function must be refinable. That is, it must be the linear combination of 2-dilation, $\mathbb{Z}$-translates of itself. Refinable functions used in connection with wavelets are…

This paper presents a detailed regularity analysis of anisotropic wavelet frames and subdivision. In the univariate setting, the smoothness of wavelet frames and subdivision is well understood by means of the matrix approach. In the…

Using a prime element of a local field K of positive characteristic p, the concepts of multiresolution analysis (MRA) and wavelet can be generalized to such a field. We prove a version of the splitting lemma for this setup and using this…

We construct multivariate p-adic L-function in the p-adic number fild by using Washington method.

We show the existence of smooth band-limited multiresolution analysis (MRA) for any expansive dilation with real entries in any spatial dimension. We then prove the existence of orthonormal Meyer wavelets, which have smooth and compactly…

Motivated by the Cauchy--Szeg\H{o} projections on a broad class of Siegel domains and the geometric quotient structures of nilpotent Lie groups observed by Nagel, Ricci, and Stein, we develop a martingale and Haar wavelet framework for…

In this paper adapting to $p$-adic case some methods of real valued Gibbs measures on Cayley trees we construct several $p$-adic distributions on the set $\mathbb{Z}_p$ of $p$-adic integers. Moreover, we give conditions under which these…

The goal of this article is to construct explicitly a p-adic family of representations (which are dihedral representations), to construct their associated (phi,Gamma)-modules by writing down explicit matrices for phi and for the action of…