The Kolmogorov Ideas on the Integration Theory in Modern Research

IF 0.2 Q4 MATHEMATICS

Moscow University Mathematics Bulletin Pub Date : 2024-05-13 DOI:10.3103/s0027132224700037

T. P. Lukashenko, V. A. Skvortsov, A. P. Solodov

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.

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现代研究中的科尔莫戈罗夫整合理论思想

摘要本文考虑了将科尔莫哥罗德积分的构造推广到巴拿赫空间值函数的情况。我们证明了关于积分理论的柯尔莫哥洛夫思想，特别是微分等价概念，是如何在亨斯托克-库兹韦尔积分理论中得到发展的。在这方面，研究了相对于相当一般的推导基础的亨斯托克型积分的变分版本。举例说明了这种积分在谐波分析中的应用。此外，还考虑了一些与科尔莫格罗夫（Kolmogorov）（A\）积分相关的结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Moscow University Mathematics Bulletin MATHEMATICS-

CiteScore

0.60

自引率

25.00%

发文量

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.