Multidimensional ultrametric pseudodifferential equations
نویسندگان
چکیده
منابع مشابه
A ug 2 00 7 Multidimensional ultrametric pseudodifferential equations
We develop an analysis of wavelets and pseudodifferential operators on multidimen-sional ultrametric spaces which are defined as products of locally compact ultrametric spaces. We introduce bases of wavelets, spaces of generalized functions and Lizorkin generalized functions on multidimensional ultrametric spaces. We also consider some family of pseudodifferential operators on multidimensional ...
متن کاملAsymptotic solutions of pseudodifferential wave equations
The aim of this paper is to give an account of some applications of pseudodifferential calculus for solving linear wave equations in the limit of high frequency/short wavelength waves. More specifically, on using as a benchmark the case of electromagnetic waves propagating in a cold isotropic slowly spaceand time-varying plasma, it is shown that, in general, linear plasma waves are governed by ...
متن کاملUltrametric pseudodifferential operators and wavelets for the case of non homogeneous measure
A new way of construction of ultrametric spaces of quite general form by completion of directed trees with respect to the metric, defined in the special way, is proposed. We introduce a measure on the constructed ultrametric space, such that the measure of any ball is positive. A family of orthonormal bases of ultrametric wavelets in the space of quadratically integrable with respect to the def...
متن کاملFe b 20 05 Ultrametric pseudodifferential operators and wavelets for the case of non homogeneous measure
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 operators (PDO) on the ultrametric space are investigated. We prove that these operators are diagonal in the introduced bases of ultrametric wavelets and com...
متن کاملPseudodifferential equations on the sphere with spherical splines
Spherical splines are used to define approximate solutions to strongly elliptic pseudodifferential equations on the unit sphere. These equations arise from geodesy. The approximate solutions are found by using Galerkin method. We prove optimal convergence (in Sobolev norms) of the approximate solution by spherical splines to the exact solution. Our numerical results underlie the theoretical res...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Steklov Institute of Mathematics
سال: 2009
ISSN: 0081-5438,1531-8605
DOI: 10.1134/s0081543809020023