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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2014, Volume 284, Pages 138–141
DOI: https://doi.org/10.1134/S0371968514010075 (Mi tm3521) 		 
This article is cited in 4 scientific papers (total in 4 papers)

On the properties of orthorecursive expansions with respect to subspaces

V. V. Galatenko, T. P. Lukashenko, V. A. Sadovnichii

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics, Moscow, Russia
Full-text PDF (140 kB) Citations (4)
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DOI: https://doi.org/10.1134/S0371968514010075
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.
Received in May 2013
English version:
Proceedings of the Steklov Institute of Mathematics, 2014, Volume 284, Pages 129–132
DOI: https://doi.org/10.1134/S0081543814010076
Bibliographic databases:
Document Type: Article
UDC: 517.98+517.51
Language: Russian
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
Citation in format AMSBIB
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\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
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    • This publication is cited in the following 4 articles:
    1. P. A. Terekhin, “Ortorekursivnye razlozheniya, porozhdennye yadrom Sege”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 23:4 (2023), 443–455  mathnet  crossref
    2. K. S. Speransky, P. A. Terekhin, “On existence of frames based on the Szegö kernel in the Hardy space”, Russian Math. (Iz. VUZ), 63:2 (2019), 51–61  mathnet  crossref  crossref  isi
    3. P. A. Terekhin, “Affine Riesz bases and the dual function”, Sb. Math., 207:9 (2016), 1287–1318  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    4. Kh. Kh. Kh. Al-Dzhourani, V. A. Mironov, P. A. Terekhin, “Affinnye sistemy funktsii tipa Uolsha. Polnota i minimalnost”, Izv. Sarat. un-ta. Nov. ser. Ser.: Matematika. Mekhanika. Informatika, 16:3 (2016), 247–256  mathnet  crossref  mathscinet  elib
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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