Optimal recovery of elements from Hilbert space and their scalar products by Fourier coefficients known with error

• Date: 2020
• Main Authors: Gunko, M. S., Babenko, V. F., Parfinovych, N. V., Гунько, М. С., Бабенко, В. Ф., Парфинович, Н. В., Парфінович, Н. В.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2020
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1107
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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...