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Funktsional'nyi Analiz i ego Prilozheniya, 2018, Volume 52, Issue 1, Pages 43–55
DOI: https://doi.org/10.4213/faa3505 (Mi faa3505) 		 
This article is cited in 1 scientific paper (total in 2 paper)

Summation of Unordered Arrays

E. V. Shchepin

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow, Russia
Full-text PDF (213 kB) Citations (2)
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DOI: https://doi.org/10.4213/faa3505
Abstract: An approach to the summation of unordered number and matrix arrays based on ordering them by absolute value (greedy summation) is proposed. Theorems on products of greedy sums are proved. A relationship between the theory of greedy summation and the theory of generalized Dirichlet series is revealed. The notion of asymptotic Dirichlet series is considered.
Keywords: greedy sum, unordered sum, theorem on multiplications of sums, generalized Dirichlet series, asymptotic Dirichlet series, Riesz means, generic zeta-function.
Funding agency Grant number
Russian Science Foundation 14-50-00005
This work was supported by the Russian Science Foundation (project No. 14-50-00005).
Received: 29.09.2016
Revised: 20.06.2017
English version:
Functional Analysis and Its Applications, 2018, Volume 52, Issue 1, Pages 35–44
DOI: https://doi.org/10.1007/s10688-018-0204-9
Bibliographic databases:
Document Type: Article
UDC: 517.537.6
Language: Russian
Citation: E. V. Shchepin, “Summation of Unordered Arrays”, Funktsional. Anal. i Prilozhen., 52:1 (2018), 43–55; Funct. Anal. Appl., 52:1 (2018), 35–44
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/faa/v52/i1/p43
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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