Real, complex and functional analysis

The discrete Wiener–Hopf equation with submultiplicative asymptotics of the solution

M. S. Sgibnev

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

Abstract: The discrete Wiener–Hopf equation is considered whose kernel is an arithmetic probability distribution with positive mean. The nonhomogeneous term behaves like a nondecreasing submultiplicative sequence. Asymptotic properties of the solution are established depending on the asymptotics of the submultiplicative sequence.

Keywords: discrete Wiener–Hopf equation, nonhomogeneous equation, arithmetic probability distribution, positive mean, submultiplicative sequence, regularly varying function, asymptotic behavior.

UDC: 517.968

MSC: 45E10

Received July 1, 2019, published November 5, 2019

DOI: 10.33048/semi.2019.16.111

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