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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     author = {G. G. Magaril-Il'yaev and E. O. Sivkova},
     title = {On the {Best} {Recovery} of a {Family} of {Operators} on the {Manifold} $\mathbb R^n\times \mathbb T^m$},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {196--203},
     publisher = {mathdoc},
     volume = {323},
     year = {2023},
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     url = {http://geodesic.mathdoc.fr/item/TM_2023_323_a10/}
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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/