Optimal Recovery of Elements of a Hilbert Space and their Scalar Products According to the Fourier Coefficients Known with Errors

In a Hilbert space defined as the image of a unit ball under the action of a compact operator, we solve the problems of optimal recovery of elements according to their first n Fourier coefficients known with errors. Similar problems are also solved for the scalar products of elements from two differ...

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Bibliographic Details
Published inUkrainian mathematical journal Vol. 72; no. 6; pp. 853 - 870
Main Authors Babenko, V. F., Gunko, M. S., Parfinovych, N. V.
Format Journal Article
LanguageEnglish
Published New York Springer US 01.11.2020
Subjects
Algebra
Analysis
Applications of Mathematics
Geometry
Mathematics
Mathematics and Statistics
Statistics
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Summary:In a Hilbert space defined as the image of a unit ball under the action of a compact operator, we solve the problems of optimal recovery of elements according to their first n Fourier coefficients known with errors. Similar problems are also solved for the scalar products of elements from two different classes.
ISSN:0041-5995
1573-9376
DOI:10.1007/s11253-020-01828-4