Geodesic
Optimal recovery of fractional powers of the Laplace difference operator
Sbornik. Mathematics, Tome 216 (2025) no. 3, pp. 445-455

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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, extremal problem.
Mots-clés : Fourier transform 
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     author = {E. O. Sivkova},
     title = {Optimal recovery of fractional powers of the {Laplace} difference operator},
     journal = {Sbornik. Mathematics},
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     number = {3},
     year = {2025},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_2025_216_3_a11/}
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E. O. Sivkova. Optimal recovery of fractional powers of the Laplace difference operator. Sbornik. Mathematics, Tome 216 (2025) no. 3, pp. 445-455. http://geodesic.mathdoc.fr/item/SM_2025_216_3_a11/