{"title":"On the combination of Lebesgue and Riemann integrals in theory of convolution equations","authors":"N. B. Engibaryan","doi":"10.1134/s0040577924010057","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p> 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. </p>","PeriodicalId":797,"journal":{"name":"Theoretical and Mathematical Physics","volume":null,"pages":null},"PeriodicalIF":1.0000,"publicationDate":"2024-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical and Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://doi.org/10.1134/s0040577924010057","RegionNum":4,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0
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.
期刊介绍：
Theoretical and Mathematical Physics covers quantum field theory and theory of elementary particles, fundamental problems of nuclear physics, many-body problems and statistical physics, nonrelativistic quantum mechanics, and basic problems of gravitation theory. Articles report on current developments in theoretical physics as well as related mathematical problems.
Theoretical and Mathematical Physics is published in collaboration with the Steklov Mathematical Institute of the Russian Academy of Sciences.
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