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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Veröffentlicht in:	Ukrainian mathematical journal 2020-11, Vol.72 (6), p.853-870
Hauptverfasser:	Babenko, V. F., Gunko, M. S., Parfinovych, N. V.
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Analysis Applications of Mathematics Geometry Mathematics Mathematics and Statistics Mathematics, Applied Physical Sciences Science & Technology Statistics
Online-Zugang:	Volltext
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Zusammenfassung:	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