{"title":"On Conditions for the Well-Posed Solvability\nof a Factorization Problem and a Class\nof Truncated Wiener–Hopf Equations","authors":"A. F. Voronin","doi":"10.1134/S1990478924030177","DOIUrl":null,"url":null,"abstract":"<p> This paper continues the study of the relationship between the convolution equation of the\nsecond kind on a finite interval\n<span>\\( (0, \\tau ) \\)</span> (which is also called the truncated Wiener–Hopf equation) and\na factorization problem (which is also called a vector Riemann–Hilbert boundary value problem or\na vector Riemann boundary value problem). The factorization problem is associated with a family\nof truncated Wiener–Hopf equations depending on the parameter\n<span>\\( \\tau \\in (0,\\infty ) \\)</span>. The well-posed solvability of this family of equations is shown depending on\nthe existence of a canonical factorization of some matrix function. In addition, various possible\napplications of the factorization problem and truncated Wiener–Hopf equations are considered.\n</p>","PeriodicalId":607,"journal":{"name":"Journal of Applied and Industrial Mathematics","volume":"18 3","pages":"575 - 582"},"PeriodicalIF":0.5800,"publicationDate":"2024-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Applied and Industrial Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://link.springer.com/article/10.1134/S1990478924030177","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Engineering","Score":null,"Total":0}
引用次数: 0
Abstract
This paper continues the study of the relationship between the convolution equation of the
second kind on a finite interval
\( (0, \tau ) \) (which is also called the truncated Wiener–Hopf equation) and
a factorization problem (which is also called a vector Riemann–Hilbert boundary value problem or
a vector Riemann boundary value problem). The factorization problem is associated with a family
of truncated Wiener–Hopf equations depending on the parameter
\( \tau \in (0,\infty ) \). The well-posed solvability of this family of equations is shown depending on
the existence of a canonical factorization of some matrix function. In addition, various possible
applications of the factorization problem and truncated Wiener–Hopf equations are considered.
期刊介绍：
Journal of Applied and Industrial Mathematics is a journal that publishes original and review articles containing theoretical results and those of interest for applications in various branches of industry. The journal topics include the qualitative theory of differential equations in application to mechanics, physics, chemistry, biology, technical and natural processes; mathematical modeling in mechanics, physics, engineering, chemistry, biology, ecology, medicine, etc.; control theory; discrete optimization; discrete structures and extremum problems; combinatorics; control and reliability of discrete circuits; mathematical programming; mathematical models and methods for making optimal decisions; models of theory of scheduling, location and replacement of equipment; modeling the control processes; development and analysis of algorithms; synthesis and complexity of control systems; automata theory; graph theory; game theory and its applications; coding theory; scheduling theory; and theory of circuits.
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