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Matematicheskie Zametki, 1975, Volume 17, Issue 5, Pages 681–690 (Mi mzm7587)  
On a property of complete orthonormal systems

N. B. Pogosyan

M. V. Lomonosov Moscow State University
Full-text PDF (589 kB)
Abstract: In this paper we establish a necessary and sufficient condition for orthonormal systems, subject to which there exist rearranged series $\Sigma_\sigma a_n\varphi_n(x)$ converging almost everywhere to functions $h(x)\overline\in L_2[0,1]$. In particular, we show, for an arbitrary complete orthonormal system, that such series exist.
Received: 09.01.1974
English version:
Mathematical Notes, 1975, Volume 17, Issue 5, Pages 405–410
DOI: https://doi.org/10.1007/BF01155793
Bibliographic databases:
UDC: 517
Language: Russian
Citation: N. B. Pogosyan, “On a property of complete orthonormal systems”, Mat. Zametki, 17:5 (1975), 681–690; Math. Notes, 17:5 (1975), 405–410
Citation in format AMSBIB
\Bibitem{Pog75}
\by N.~B.~Pogosyan
\paper On a~property of complete orthonormal systems
\jour Mat. Zametki
\yr 1975
\vol 17
\issue 5
\pages 681--690
\mathnet{http://mi.mathnet.ru/mzm7587}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=394025}
\zmath{https://zbmath.org/?q=an:0327.42010|0318.42025}
\transl
\jour Math. Notes
\yr 1975
\vol 17
\issue 5
\pages 405--410
\crossref{https://doi.org/10.1007/BF01155793}
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