On the combination of Lebesgue and Riemann integrals in theory of convolution equations

N. B. Engibaryan

Institute of Mathematics, NAS RA, Yerevan, Armenia

Abstract: Using the example of scalar and vector Wiener–Hopf equations, we consider two methods for combining the options for the Riemann integral and Lebesgue functional spaces in problems of studying and solving integral convolution equations. The method of nonlinear factorization equations and the kernel averaging method are used. A generalization of the direct Riemann integrability is introduced and applied.

Keywords: improper direct Riemann integrability, Wiener–Hopf equation, nonlinear factorization equation, kernel averaging method.

Received: 08.06.2023
Revised: 08.06.2023

DOI: 10.4213/tmf10565

 English version: Theoretical and Mathematical Physics, 2024, 218:1, 68–74

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