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Izv. RAN. Ser. Mat., 2009, Volume 73, Issue 2, Pages 69–90 (Mi izv2618)  

This article is cited in 1 scientific paper (total in 1 paper)

On absolute and unconditional convergence of series in the general Franklin system

G. G. Gevorkyan, K. A. Kerian

Yerevan State University

Abstract: We prove that, for any admissible sequence, the corresponding general Franklin system $\{f_n(x)\}_{n=0}^{\infty}$ possesses the following property. A series $\sum_{n=0}^{\infty}a_nf_n(x)$ is absolutely convergent almost everywhere on a set $E$ if and only if it is unconditionally convergent almost everywhere on $E$.

Keywords: series, general Franklin system, absolute convergence, unconditional convergence.

DOI: https://doi.org/10.4213/im2618

Full text: PDF file (559 kB)
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English version:
Izvestiya: Mathematics, 2009, 73:2, 279–300

Bibliographic databases:

UDC: 517.51
MSC: 42C10, 42C15, 40A30
Received: 15.02.2007

Citation: G. G. Gevorkyan, K. A. Kerian, “On absolute and unconditional convergence of series in the general Franklin system”, Izv. RAN. Ser. Mat., 73:2 (2009), 69–90; Izv. Math., 73:2 (2009), 279–300

Citation in format AMSBIB
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  • https://doi.org/10.4213/im2618
  • http://mi.mathnet.ru/eng/izv/v73/i2/p69

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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. Gevorkyan G.G., “On Series by General Franklin System”, J. Contemp. Math. Anal.-Armen. Aca., 48:5 (2013), 189–208  crossref  mathscinet  zmath  isi
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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