This article is cited 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

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.

UDC: 517.518.43

Received: 27.04.2016

 English version: Moscow University Mathematics Bulletin, Moscow University Mеchanics Bulletin, 2017, 72:1, 24–30

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