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.
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, No. 6, pp. 736–750, June, 2020. Ukrainian DOI: 10.37863/umzh.v72i6.1107.
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Babenko, V.F., Gunko, M.S. & Parfinovych, N.V. Optimal Recovery of Elements of a Hilbert Space and their Scalar Products According to the Fourier Coefficients Known with Errors. Ukr Math J 72, 853–870 (2020). https://doi.org/10.1007/s11253-020-01828-4
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DOI: https://doi.org/10.1007/s11253-020-01828-4