{"title":"The Kolmogorov Ideas on the Integration Theory in Modern Research","authors":"T. P. Lukashenko, V. A. Skvortsov, A. P. Solodov","doi":"10.3103/s0027132224700037","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>Generalizations of construction of Kolmogorov integral to the case of Banach space-valued functions are considered. We demonstrate how the Kolmogorov ideas on integration theory, in particular, the notion of differential equivalence, have been developed in the theory of the Henstock–Kurzweil integral. In this connection, a variational version of a Henstock type integral with respect to a rather general derivation basis is studied. An example of application of this integral to harmonic analysis is given. Some results related to the Kolmogorov <span>\\(A\\)</span>-integral are also considered.</p>","PeriodicalId":42963,"journal":{"name":"Moscow University Mathematics Bulletin","volume":null,"pages":null},"PeriodicalIF":0.2000,"publicationDate":"2024-05-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Moscow University Mathematics Bulletin","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3103/s0027132224700037","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
Generalizations of construction of Kolmogorov integral to the case of Banach space-valued functions are considered. We demonstrate how the Kolmogorov ideas on integration theory, in particular, the notion of differential equivalence, have been developed in the theory of the Henstock–Kurzweil integral. In this connection, a variational version of a Henstock type integral with respect to a rather general derivation basis is studied. An example of application of this integral to harmonic analysis is given. Some results related to the Kolmogorov \(A\)-integral are also considered.
期刊介绍：
Moscow University Mathematics Bulletin is the journal of scientific publications reflecting the most important areas of mathematical studies at Lomonosov Moscow State University. The journal covers research in theory of functions, functional analysis, algebra, geometry, topology, ordinary and partial differential equations, probability theory, stochastic processes, mathematical statistics, optimal control, number theory, mathematical logic, theory of algorithms, discrete mathematics and computational mathematics.
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