Integration of Banach-valued functions and Haar series with Banach-valued coefficients

It is proved that for any Banach space each everywhere convergent Haar series with coefficients from this space is the Fourier–Haar series in the sense of Henstock type integral with respect to a dyadic differential basis. At the same time, the almost everywhere convergence of a Fourier–Henstock–Haa...

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Bibliographic Details
Published inMoscow University mathematics bulletin Vol. 72; no. 1; pp. 24 - 30
Main Author Skvortsov, V. A.
Format Journal Article
LanguageEnglish
Published New York Allerton Press 2017
Springer Nature B.V
Subjects
Analysis
Fourier series
Mathematics
Mathematics and Statistics
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Summary:It is proved that for any Banach space each everywhere convergent Haar series with coefficients from this space is the Fourier–Haar series in the sense of Henstock type integral with respect to a dyadic differential basis. At the same time, the almost everywhere convergence of a Fourier–Henstock–Haar series of a Banach-space-valued function essentially depends on properties of the space.
ISSN:0027-1322
1934-8444
DOI:10.3103/S0027132217010041