Optimal recovery of fractional powers of the Laplace difference operator

E. O. Sivkova<sup>ab

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

Abstract: The concept of a fractional power of the Laplace difference operator of a function on an $d$-dimensional lattice is introduced, and the problem of optimal recovery from inaccurate information about the function itself is stated for this fractional power. A family of optimal recovery methods is constructed.
Bibliography: 11 titles.

Keywords: Laplace difference operator, optimal recovery, optimal method, Fourier transform, extremal problem.

MSC: Primary 49N30; Secondary 42B10

Received: 17.09.2024 and 13.11.2024

DOI: 10.4213/sm10196

 English version: Sbornik: Mathematics, 2025, 216:3, 445–455

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