Electron. J. Differential Equations, Vol. 2017 (2017), No. 216, pp. 1-9.

Convolutions with probability densities and applications to PDEs

Sorin G. Gal

In this article we 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 example in the heat or Laplace equations), we deduce the initial and final value problems satisfied by the new convolution integrals.

Submitted April 4, 2017. Published September 13, 2017.
Math Subject Classifications: 44A35, 35A22, 35C15.
Key Words: Probability density; convolution integral; Fourier transform; initial value problem; final value problem.

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Sorin G. Gal
University of Oradea
Department of Mathematics and Computer Science
Str. Universitatii 1
410087 Oradea, Romania
email: galsorin23@gmail.com

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