Real, complex and functional analysis

The Wiener–Hopf equation in measures with probability kernel

M. S. Sgibnev

Sobolev Institute of Mathematics, 4, Koptyuga ave., Novosibirsk, 630090, Russia

Abstract: The paper deals with a generalization of the classical Wiener–Hopf equation where the functions involved are replaced by measures. A solution in explicit form is given, which coincides with the solution found by the method of successive approximations. An asymptotic property of the solution is also established.

Keywords: integral equation, measure, Wiener–Hopf equation, probability distribution, asymptotic behavior.

UDC: 517.968

MSC: 45E10

Received February 26, 2019, published April 30, 2019

DOI: 10.33048/semi.2019.16.039

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