English

Approximation by convolutions with probability densities and applications to PDEs

Classical Analysis and ODEs 2017-09-15 v2

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.

Keywords

Cite

@article{arxiv.1702.08499,
  title  = {Approximation by convolutions with probability densities and applications to PDEs},
  author = {Sorin G. Gal},
  journal= {arXiv preprint arXiv:1702.08499},
  year   = {2017}
}

Comments

11 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)

R2 v1 2026-06-22T18:29:58.385Z