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Mat. Sb., 1994, Volume 185, Number 7, Pages 109–118 (Mi msb914)  

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

On the theory of singular expansion in a tensor product of Hilbert spaces

V. V. Pospelov


Abstract: Approximation of an element in a tensor product of Hilbert spaces by a sum of products of elements in each of these spaces is considered. The existence of best approximation and the convergence of bilinear series are proved. An explicit representation for the best approximation is obtained. Analogous results in the Sobolev spaces $W_2^{p,q}(\Pi)$ are given as corollaries.

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English version:
Russian Academy of Sciences. Sbornik. Mathematics, 1995, 82:2, 357–364

Bibliographic databases:

UDC: 517.98
MSC: Primary 41A65, 46B28; Secondary 46E35
Received: 20.07.1993

Citation: V. V. Pospelov, “On the theory of singular expansion in a tensor product of Hilbert spaces”, Mat. Sb., 185:7 (1994), 109–118; Russian Acad. Sci. Sb. Math., 82:2 (1995), 357–364

Citation in format AMSBIB
\Bibitem{Pos94}
\by V.~V.~Pospelov
\paper On the theory of singular expansion in a~tensor product of Hilbert spaces
\jour Mat. Sb.
\yr 1994
\vol 185
\issue 7
\pages 109--118
\mathnet{http://mi.mathnet.ru/msb914}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1300135}
\zmath{https://zbmath.org/?q=an:0854.46019}
\transl
\jour Russian Acad. Sci. Sb. Math.
\yr 1995
\vol 82
\issue 2
\pages 357--364
\crossref{https://doi.org/10.1070/SM1995v082n02ABEH003569}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=A1995RV83000007}


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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. I. Kutchinsky, “An error estimation in $\Sigma\Pi$-approximation via statistical methods”, Sib. zhurn. vychisl. matem., 2:1 (1999), 37–46  mathnet  zmath
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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