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Mat. Zametki, 1976, Volume 19, Issue 5, Pages 673–680 (Mi mz7787)  

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

The representations of functions by orthogonal series possessing martingale properties

R. S. Davtyan

Mathematics Institute, Academy of Sciences of the Armenian SSR

Abstract: Let $\mathscr F_\infty$ be the minimal $\sigma$-algebra generated by the orthogonal system $\{\varphi_n(x)\}$, defined on the space $(X,S,\mu)$ of finite measure. For a certain class of orthonormal systems one proves that for any $\mathscr F_\infty$-measurable function $f(x)$, which is finite almost everywhere, there exists a series $\sum_{n=1}^\infty a_n\varphi_n(x)$ which converges absolutely to $f(x)$ almost everywhere. This result represents an extension of a theorem by R. Gundy on the representation of functions by orthogonal series possessing martingale properties.

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English version:
Mathematical Notes, 1976, 19:5, 405–409

Bibliographic databases:

Received: 26.05.1975

Citation: R. S. Davtyan, “The representations of functions by orthogonal series possessing martingale properties”, Mat. Zametki, 19:5 (1976), 673–680; Math. Notes, 19:5 (1976), 405–409

Citation in format AMSBIB
\Bibitem{Dav76}
\by R.~S.~Davtyan
\paper The representations of functions by orthogonal series possessing martingale properties
\jour Mat. Zametki
\yr 1976
\vol 19
\issue 5
\pages 673--680
\mathnet{http://mi.mathnet.ru/mz7787}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=422987}
\zmath{https://zbmath.org/?q=an:0349.42015|0338.42012}
\transl
\jour Math. Notes
\yr 1976
\vol 19
\issue 5
\pages 405--409
\crossref{https://doi.org/10.1007/BF01142560}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. K. A. Navasardyan, “O predstavlenii funktsii absolyutno skhodyaschimisya ryadami po $\mathcal{H}$-sistemam”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 18:1 (2018), 49–61  mathnet  crossref  elib
  • Математические заметки Mathematical Notes
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