Approximation by convolutions with probability densities and applications to PDEs

Abstract

The purpose of this paper is to introduce several new convolution operators, generated by some known probability densities. By using the inverse Fourier transform and taking inverse steps (in the analogues of the classical procedures used for, e.g., the heat or Laplace equations), we deduce the initial and final value problems satisfied by the new convolution integrals.

arXiv comment11 pages, "TO PDEs" added to the title, Section 4 deleted, some changes made in Definition 2.1, (iv) and (v) and in Theorem 3.1, (iv) and (v)