{"title":"Representations of Solutions for Volterra Integro-Differential Equations in Hilbert Spaces","authors":"N. A. Rautian","doi":"10.1134/S1064562424601240","DOIUrl":null,"url":null,"abstract":"<p>Volterra integro-differential equations with operator coefficients in Hilbert spaces are studied. Previously obtained results are used to establish the relationship between the spectra of operator functions that are the symbols of the specified integro-differential equations and the spectra of generators of operator semigroups. Representations of solutions for the considered integro-differential equations are obtained on the basis of spectral analysis of generators of operator semigroups and corresponding operator functions.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"109 3","pages":"262 - 267"},"PeriodicalIF":0.5000,"publicationDate":"2024-07-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Doklady Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1134/S1064562424601240","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Volterra integro-differential equations with operator coefficients in Hilbert spaces are studied. Previously obtained results are used to establish the relationship between the spectra of operator functions that are the symbols of the specified integro-differential equations and the spectra of generators of operator semigroups. Representations of solutions for the considered integro-differential equations are obtained on the basis of spectral analysis of generators of operator semigroups and corresponding operator functions.
期刊介绍：
Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.
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