Optimal recovery of linear operators on a homogeneous Sobolev space

E. O. Sivkova<sup>ab

a</sup> Southern Mathematical Institute of the Vladikavkaz Scientific Center of the Russian Academy of Sciences, Vladikavkaz
^b National Research University "Moscow Power Engineering Institute"

Abstract: For a one-parameter family of linear operators, given an operator on a homogeneous Sobolev space with given value of the parameter, we consider the problem of optimal recovery of this operator from incomplete information about this operator with a different value of the parameter. A family of optimal recovery methods is constructed. As a corollary, we obtain optimal methods of recovery of solutions to some equations of mathematical physics.

Keywords: optimal recovery, optimal method, Fourier transform, extremal problem.

UDC: 517.9

Received: 05.07.2024
Revised: 09.08.2024

DOI: 10.4213/mzm14435

 English version: Mathematical Notes, 2025, 117:6, 1065–1078

Bibliographic databases:

•