Geodesic
On the Best Recovery of a Family of Operators on the Manifold $\mathbb R^n\times \mathbb T^m$
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Theory of Functions of Several Real Variables and Its Applications, Tome 323 (2023), pp. 196-203.

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Given a one-parameter family of operators on the manifold $\mathbb R^n\times \mathbb T^m$, we solve the problem of the best recovery of an operator for a given value of the parameter from inaccurate data on the operators for other values of the parameter from a certain compact set. We construct a family of best recovery methods. As a consequence, we obtain families of best recovery methods for the solutions of the heat equation and the Dirichlet problem for a half-space.
Keywords: best recovery, optimal method, extremum problem.
Mots-clés : Fourier transform 
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G. G. Magaril-Il'yaev; E. O. Sivkova. On the Best Recovery of a Family of Operators on the Manifold $\mathbb R^n\times \mathbb T^m$. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Theory of Functions of Several Real Variables and Its Applications, Tome 323 (2023), pp. 196-203. http://geodesic.mathdoc.fr/item/TM_2023_323_a10/

[1] E. V. Abramova, G. G. Magaril-Il'yaev, and E. O. Sivkova, “Best recovery of the solution of the Dirichlet problem in a half-space from inaccurate data”, Comput. Math. Math. Phys., 60:10 (2020), 1656–1665 | DOI | MR | Zbl

[2] G. G. Magaril-Il'yaev and K. Yu. Osipenko, “Optimal recovery of the solution of the heat equation from inaccurate data”, Sb. Math., 200:5 (2009), 665–682 | DOI | DOI | MR | Zbl

[3] G. G. Magaril-Il'yaev, K. Yu. Osipenko, and E. O. Sivkova, “Optimal recovery of pipe temperature from inaccurate measurements”, Proc. Steklov Inst. Math., 312 (2021), 207–214 | DOI | DOI | MR | Zbl

[4] Magaril-Il'yaev G.G., Sivkova E.O., “Optimal recovery of semi-group operators from inaccurate data”, Eurasian Math. J., 10:4 (2019), 75–84 | DOI | MR | Zbl

[5] G. G. Magaril-Il'yaev and V. M. Tikhomirov, Convex Analysis: Theory and Applications, Transl. Math. Monogr., 222, Am. Math. Soc., Providence, RI, 2003 | MR | MR | Zbl