Optimal recovery of elements from Hilbert space and their scalar products by Fourier coefficients known with error - Gunko, M. S.; Babenko, V. F.; Parfinovych, N. V.; Гунько, М. С.; Бабенко, В. Ф.; Парфинович, Н. В.; Гунько, М. С.; Бабенко, В. Ф.; Парфінович, Н. В. (Institute of Mathematics, NAS of Ukraine, 2020)
UDC 517.5 In a Hilbert space defined as the image of the unit ball under the action of a compact operator, we solve problems of optimal recovery of elements by their first $n$ Fourier coefficients given approximately. Similar problems are also solved for scalar products of elements from two different classes.