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Izv. Akad. Nauk SSSR Ser. Mat., 1978, Volume 42, Issue 4, Pages 807–832 (Mi izv1847)  

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

On the coefficients of everywhere convergent series in some rearranged orthonormal systems

G. M. Mushegyan


Abstract: In this paper the author establishes the existence of a series $\sum a_{\nu_k}\cos\nu_kx+b_{\nu_k}\sin\nu_kx$ in some rearranged trigonometric system, which converges everywhere to a Lebesgue integrable function and whose coefficients $a_{\nu_k}$ and $b_{\nu_k}$, $k=1,2,…$, are not the Fourier–Lebesgue coefficients of this function. Similar results are established for the Haar system and some other systems.
Bibliography: 17 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1979, 13:1, 107–132

Bibliographic databases:

UDC: 517.5
MSC: Primary 42C20; Secondary 42C25
Received: 01.03.1976

Citation: G. M. Mushegyan, “On the coefficients of everywhere convergent series in some rearranged orthonormal systems”, Izv. Akad. Nauk SSSR Ser. Mat., 42:4 (1978), 807–832; Math. USSR-Izv., 13:1 (1979), 107–132

Citation in format AMSBIB
\Bibitem{Mus78}
\by G.~M.~Mushegyan
\paper On the coefficients of everywhere convergent series in some rearranged orthonormal systems
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1978
\vol 42
\issue 4
\pages 807--832
\mathnet{http://mi.mathnet.ru/izv1847}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=508828}
\zmath{https://zbmath.org/?q=an:0421.42014|0388.42007}
\transl
\jour Math. USSR-Izv.
\yr 1979
\vol 13
\issue 1
\pages 107--132
\crossref{https://doi.org/10.1070/IM1979v013n01ABEH002014}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1979JB17800007}


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  • http://mi.mathnet.ru/eng/izv/v42/i4/p807

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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. G. M. Mushegyan, “On the recovery of the coefficients of a rearranged Haar series”, Math. USSR-Sb., 58:1 (1987), 31–57  mathnet  crossref  mathscinet  zmath
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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