Summability of spectral expansions of distributions
by
Rakhimov Abdumalik
FUUAST, Karachi, Pakistan

It is well known that classical analysis deals with the smooth or piecewise smooth functions. But many phenomena in nature require for its description either "bad" functions or even they can not be described by regular functions. Therefore, one has to deal with distributions that describe only integral characteristics of phenomena. Theory of distributions provides a powerful tool in formulation and solution of the problems in nature. It has many applications for describing the problems in science and engineering.

Application of the modern methods of mathematical physics in the spaces of distributions, leads to the convergence and sumability problems of spectral expansions of distributions. The convergence and sumability problems of spectral expansions of distributions, associated with partial differential operators, connected with the development of mathematical tools for modern science and engineering.

We study convergence and summability problems of spectral expansions of distributions in classical means in the domain where they coincide with regular functions. But singularities of the distribution still will be essential for convergence problems even at regular points. It was obtained sharp conditions for localization of Riesz's means spectral decompositions of distributions.

Date received: February 24, 2008

Copyright © 2008 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caub-54.