Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika
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Vestnik Moskovskogo Universiteta. Seriya 1. Matematika. Mekhanika, 2017, Number 1, Pages 25–32 (Mi vmumm40)  
This article is cited in 2 scientific papers (total in 2 papers)

Mathematics

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

V. A. Skvortsov

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (327 kB) Citations (2)
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Abstract: 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 a Henstock type integral with respect to dyadic derivation basis. At the same time convergence of Fourier–Henstock–Haar series Banach-space-valued functions is essentially dependent on properties of a space.
Key words: Haar series, Walsh series, dyadic derivation basis, Henstock integral, Pettis integral, Banach-space-valued functions, Orlicz property.
Funding agency Grant number
Russian Foundation for Basic Research 17-01-00286
Received: 27.04.2016
English version:
Moscow University Mathematics Bulletin, 2017, Volume 72, Issue 1, Pages 24–30
DOI: https://doi.org/10.3103/S0027132217010041
Bibliographic databases:
Document Type: Article
UDC: 517.518.43
Language: Russian
Citation: V. A. Skvortsov, “Integration of Banach-valued functions and Haar series with Banach-valued coefficients”, Vestnik Moskov. Univ. Ser. 1. Mat. Mekh., 2017, no. 1, 25–32; Moscow University Mathematics Bulletin, 72:1 (2017), 24–30
Citation in format AMSBIB
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    • This publication is cited in the following 2 articles:
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