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GENERALIZED WIENER–HOPF EQUATIONS WITH DIRECTLY RIEMANN INTEGRABLE INHOMOGENEOUS TERM

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Abstract

We establish the asymptotic behavior of the solution to the generalized Wiener–Hopf equation whose kernel is a probability distribution, whereas the inhomogeneous term is a directly Riemann integrable function. To this end, we prove that the convolution of a finite measure and a directly Riemann integrable function is also a directly Riemann integrable function.

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  1. Sobolev Institute of Mathematics, Novosibirsk, Russia

    M.S. Sgibnev

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  1. M.S. Sgibnev
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Correspondence to M.S. Sgibnev.

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The author declares no competing interests.

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The work was carried out within the framework of the State Task to the Sobolev Institute of Mathematics (Project FWNF-2022-0004).

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Sgibnev, M. GENERALIZED WIENER–HOPF EQUATIONS WITH DIRECTLY RIEMANN INTEGRABLE INHOMOGENEOUS TERM. J Math Sci 271, 400–405 (2023). https://doi.org/10.1007/s10958-023-06549-0

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  • DOI: https://doi.org/10.1007/s10958-023-06549-0

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