Abstract:
In a Hilbert space, for orthorecursive expansions with respect to closed subspaces, we establish a criterion for expansions of elements of a certain finite-dimensional subspace with respect to a finite sequence of subspaces to coincide with the expanded elements. This implies a criterion for an element to be equal to its orthorecursive expansion with respect to a finite sequence of subspaces. We also obtain a number of results related to the best approximations of elements by partial sums of their orthorecursive expansions with respect to a sequence of finite-dimensional subspaces.
Citation:
V. V. Galatenko, T. P. Lukashenko, V. A. Sadovnichii, “On the properties of orthorecursive expansions with respect to subspaces”, Function spaces and related problems of analysis, Collected papers. Dedicated to Oleg Vladimirovich Besov, corresponding member of the Russian Academy of Sciences, on the occasion of his 80th birthday, Trudy Mat. Inst. Steklova, 284, MAIK Nauka/Interperiodica, Moscow, 2014, 138–141; Proc. Steklov Inst. Math., 284 (2014), 129–132
\Bibitem{GalLukSad14}
\by V.~V.~Galatenko, T.~P.~Lukashenko, V.~A.~Sadovnichii
\paper On the properties of orthorecursive expansions with respect to subspaces
\inbook Function spaces and related problems of analysis
\bookinfo Collected papers. Dedicated to Oleg Vladimirovich Besov, corresponding member of the Russian Academy of Sciences, on the occasion of his 80th birthday
\serial Trudy Mat. Inst. Steklova
\yr 2014
\vol 284
\pages 138--141
\publ MAIK Nauka/Interperiodica
\publaddr Moscow
\mathnet{http://mi.mathnet.ru/tm3521}
\crossref{https://doi.org/10.1134/S0371968514010075}
\elib{https://elibrary.ru/item.asp?id=21249105}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2014
\vol 284
\pages 129--132
\crossref{https://doi.org/10.1134/S0081543814010076}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000335559000006}
\elib{https://elibrary.ru/item.asp?id=21876609}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84899819865}
Linking options:
https://www.mathnet.ru/eng/tm3521
https://doi.org/10.1134/S0371968514010075
https://www.mathnet.ru/eng/tm/v284/p138
This publication is cited in the following 4 articles:
Citation in format AMSBIB
Contact us: