Related papers: Equations For Frame Wavelets In $L^2(\R^2)$
In this series of eight papers we present the applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. In this part we consider the applications of discrete wavelet analysis…
We study continuous wavelet transforms associated to matrix dilation groups giving rise to an irreducible square-integrable quasi-regular representation on ${\rm L}^2(\mathbb{R}^d)$. We first prove that these representations are integrable…
An integral representation of solutions of the wave equation as a superposition of other solutions of this equation is built. The solutions from a wide class can be used as building blocks for the representation. Considerations are based on…
Wavelets are a useful basis for constructing solutions of the integral and differential equations of scattering theory. Wavelet bases efficiently represent functions with smooth structures on different scales, and the matrix representation…
We present applications of variational-wavelet approach to nonlinear (rational) rms envelope equations. We have the solution as a multiresolution (multiscales) expansion in the base of compactly supported wavelet basis. We give extension of…
In \cite{AV99}, Antoine and Vandergheynst propose a group-theoretic approach to continuous wavelet frames on the sphere. The frame is constructed from a single so-called admissible function by applying the unitary operators associated to a…
Simultaneous tiling for several different translational sets has been studied rather extensively, particularly in connection with the Steinhaus problem. The study of orthonormal wavelets in recent years, particularly for arbitrary dilation…
Wave Kinetic Equations (WKEs) are often used to describe the evolution of ensemble averaged wave amplitudes for nonlinear wave systems. In the present manuscript we describe a new approach to direct numerical simulation of solutions to…
Governing equations for two-dimensional inviscid free-surface flows with constant vorticity over arbitrary non-uniform bottom profile are presented in exact and compact form using conformal variables. An efficient and very accurate…
We construct a Continuous Wavelet Transform (CWT) on the torus $\mathbb T^2$ following a group-theoretical approach based on the conformal group $SO(2,2)$. The Euclidean limit reproduces wavelets on the plane $\mathbb R^2$ with two…
We study conformally compact metrics satisfying the Lovelock equations, which generalize the Einstein equation. We show that these metrics admit polyhomogeneous expansions, thereby naturally realizing the Fefferman-Graham expansion, which…
In this work we establish a weighted $L^2-L^2$ estimate for inhomogeneous wave equation in 3-D, by introducing a Morawetz multiplier with weight of power $s(1<s<2)$, and then integrating on the light cones and $t$ slice. With this weighted…
A condition of reduction of multidimensional wave equations to the two-dimensional equation is studied, and the necessary conditions of compatibility and exact solutions of the resulting d'Alembert-Hamilton system are obtained.
In the last decade, the perfectly matched layer (PML) approach has proved a flexible and accurate method for the simulation of waves in unbounded media. Most PML formulations, however, usually require wave equations stated in their standard…
We present the applications of variation -- wavelet analysis to polynomial/rational approximations for orbital motion in transverse plane for a single particle in a circular magnetic lattice in case when we take into account multipolar…
As a main research area in applied and computational harmonic analysis, the theory and applications of framelets have been extensively investigated. Most existing literature is devoted to framelet systems that only use one dilation matrix…
A new construction of decomposition smoothness spaces of homogeneous type is considered. The smoothness spaces are based on structured and flexible decompositions of the frequency space $\mathbb{R}^d\backslash\{0\}$. We construct simple…
The paper addresses the two-point correlations of electromagnetic waves in general random, bi-anisotropic media whose constitutive tensors are complex Hermitian, positive- or negative-definite matrices. A simplified version of the…
Our aim in this paper is to characterize local Muckenhoupt weighted Lebesgue spaces with variable exponent by compactly supported smooth wavelets. We also investigate necessary and sufficient conditions for the corresponding modular…
We consider (2+1) and (1+1) dimensional long-wave short-wave resonance interaction systems. We construct an extensive set of exact periodic solutions of these systems in terms of Lam\'e polynomials of order one and two. The periodic…