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On the properties of orthorecursive expansions with respect to subspaces. (English. Russian original) Zbl 1318.46012

Proc. Steklov Inst. Math. 284, 129-132 (2014); translation from Tr. Mat. Inst. Steklova 284, 138-141 (2014).
Summary: 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.

MSC:

46C05 Hilbert and pre-Hilbert spaces: geometry and topology (including spaces with semidefinite inner product)
42C99 Nontrigonometric harmonic analysis
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