On the properties of orthorecursive expansions with respect to subspaces

被引：4
|
作者：
Galatenko, V. V. [1 ]
Lukashenko, T. P. [1 ]
Sadovnichii, V. A. [1 ]
机构：
[1] Moscow MV Lomonosov State Univ, Fac Mech & Math, Moscow 119991, Russia
来源：
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2014年 / 284卷 / 01期
基金：
俄罗斯基础研究基金会;
关键词：
Hilbert Space; Fourier Series; Orthogonal Projection; STEKLOV Institute; Closed Subspace;
D O I：
10.1134/S0081543814010076
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
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.
引用
收藏
页码：129 / 132
页数：4
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