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Matematicheskie Zametki, 2015, Volume 98, Issue 1, Pages 12–26
DOI: https://doi.org/10.4213/mzm10463 (Mi mzm10463) 		 
This article is cited in 6 scientific papers (total in 6 papers)

Integration of Functions Ranging in Complex Riesz Space and Some Applications in Harmonic Analysis

A. Bokkutoa, V. A. Skvortsovb, F. Tulonec

a Università degli Studi di Perugia
b Lomonosov Moscow State University
c Università degli Studi di Palermo
Full-text PDF (603 kB) Citations (6)
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DOI: https://doi.org/10.4213/mzm10463
Abstract: The theory of Henstock–Kurzweil integral is generalized to the case of functions ranging in complex Riesz space $R$ and defined on any zero-dimensional compact Abelian group. The constructed integral is used to solve the problem of recovering the $R$-valued coefficients of series in systems of characters of these groups by using generalized Fourier formulas.
Keywords: complex Riesz space, zero-dimensional compact Abelian group, group characters, Henstock–Kurzweil integral.
Funding agency Grant number
Russian Foundation for Basic Research 14-01-00417
Ministry of Education and Science of the Russian Federation НШ-3682.2014.1
This work was supported by the Russian Foundation for Basic Research (grant no. 14-01-00417), by the program "Leading Scientific Schools" (grant no. NSh-3682.2014.1), and in part by the Institute of Mathematics at the Bydgoszcz University (UKW, Bydgoszcz, Poland).
Received: 20.03.2014
Revised: 17.01.2015
English version:
Mathematical Notes, 2015, Volume 98, Issue 1, Pages 25–37
DOI: https://doi.org/10.1134/S0001434615070032
Bibliographic databases:
Document Type: Article
UDC: 517.53+517.57
Language: Russian
Citation: A. Bokkuto, V. A. Skvortsov, F. Tulone, “Integration of Functions Ranging in Complex Riesz Space and Some Applications in Harmonic Analysis”, Mat. Zametki, 98:1 (2015), 12–26; Math. Notes, 98:1 (2015), 25–37
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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