Approximation by convolutions with probability densities and applications to PDEs

zbMATH Open1371.44005arXiv1702.08499MaRDI QIDQ5364171

Sorin G. Gal

Publication date: 4 October 2017

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.

Full work available at URL: https://arxiv.org/abs/1702.08499

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zbMATH Keywords

Fourier transformprobability densityinitial value problemconvolution integralfinal value problem

Mathematics Subject Classification ID

Convolution as an integral transform (44A35) Integral representations of solutions to PDEs (35C15) Transform methods (e.g., integral transforms) applied to PDEs (35A22)

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