Geodesic
On the properties of orthorecursive expansions with respect to subspaces
Informatics and Automation, Function spaces and related problems of analysis, Tome 284 (2014), pp. 138-141 
V. V. Galatenko; T. P. Lukashenko; V. A. Sadovnichii. On the properties of orthorecursive expansions with respect to subspaces. Informatics and Automation, Function spaces and related problems of analysis, Tome 284 (2014), pp. 138-141. http://geodesic.mathdoc.fr/item/TRSPY_2014_284_a6/
@article{TRSPY_2014_284_a6,
     author = {V. V. Galatenko and T. P. Lukashenko and V. A. Sadovnichii},
     title = {On the properties of orthorecursive expansions with respect to subspaces},
     journal = {Informatics and Automation},
     pages = {138--141},
     year = {2014},
     volume = {284},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2014_284_a6/}
}
TY  - JOUR
AU  - V. V. Galatenko
AU  - T. P. Lukashenko
AU  - V. A. Sadovnichii
TI  - On the properties of orthorecursive expansions with respect to subspaces
JO  - Informatics and Automation
PY  - 2014
SP  - 138
EP  - 141
VL  - 284
UR  - http://geodesic.mathdoc.fr/item/TRSPY_2014_284_a6/
LA  - ru
ID  - TRSPY_2014_284_a6
ER  - 
%0 Journal Article
%A V. V. Galatenko
%A T. P. Lukashenko
%A V. A. Sadovnichii
%T On the properties of orthorecursive expansions with respect to subspaces
%J Informatics and Automation
%D 2014
%P 138-141
%V 284
%U http://geodesic.mathdoc.fr/item/TRSPY_2014_284_a6/
%G ru
%F TRSPY_2014_284_a6

Voir la notice de l'article provenant de la source Math-Net.Ru

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.

[1] Lukashenko T.P., “Rekursivnye razlozheniya, podobnye ortogonalnym”, VII Mezhdunar. konf. Matematika. Ekonomika. Ekologiya. Obrazovanie, Mezhdunar. simp. Ryady Fure i ikh prilozheniya, 26 maya–1 iyunya 1999: Tez. dokl., RGEA, Rostov-na-Donu, 1999, 331

[2] Lukashenko T.P., “Ob ortorekursivnykh razlozheniyakh po kharakteristicheskim funktsiyam promezhutkov”, Teoriya funktsii, ee prilozheniya i smezhnye voprosy, Mater. Shkoly-konf., posv. 130-letiyu D.F. Egorova, Kazansk. mat. o-vo, Kazan, 1999, 142–143

[3] Lukashenko T.P., “O svoistvakh ortorekursivnykh razlozhenii po neortogonalnym sistemam”, Vestn. Mosk. un-ta. Matematika. Mekhanika, 2001, no. 1, 6–10 | MR | Zbl

[4] Lukashenko T.P., Sadovnichii V.A., “O rekursivnykh razlozheniyakh po tsepochke sistem”, DAN, 425:6 (2009), 741–746 | MR | Zbl

[5] Terekhin P.A., “Neravenstva dlya komponentov summiruemykh funktsii i ikh predstavleniya po elementam sistemy szhatii i sdvigov”, Izv. vuzov. Matematika, 1999, no. 8, 74–81 | MR | Zbl

[6] Politov A.V., “Ortorekursivnye razlozheniya v gilbertovykh prostranstvakh”, Vestn. Mosk. un-ta. Matematika. Mekhanika, 2010, no. 3, 3–7 | MR

[7] Lukashenko T.P., Sadovnichii V.A., “Ortorekursivnye razlozheniya po podprostranstvam”, DAN, 445:2 (2012), 135–138 | MR | Zbl

[8] Kolmogorov A.N., Fomin S.V., Elementy teorii funktsii i funktsionalnogo analiza, Fizmatlit, M., 2012

[9] Bogachev V.I., Smolyanov O.G., Deistvitelnyi i funktsionalnyi analiz: universitetskii kurs, In-t kompyut. issled., M.; Izhevsk, 2009