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On the optimal recovery of one family of operators on a class of functions from approximate information about its spectrum. (English. Russian original) Zbl 07825242

Sib. Math. J. 65, No. 2, 245-256 (2024); translation from Sib. Mat. Zh. 65, No. 2, 235-248 (2024).
Summary: We find explicit expressions for optimal recovery methods in the problem of recovering the values of continuous linear operators on a Sobolev function class from the following information: The Fourier transform of functions is known approximately on some measurable subset of the finite-dimensional space on which the functions are defined. As corollaries, we obtain optimal methods for recovering the solution to the heat equation and solving the Dirichlet problem for a half-space.

MSC:

41Axx Approximations and expansions
42Bxx Harmonic analysis in several variables
46Exx Linear function spaces and their duals
42B10 Fourier and Fourier-Stieltjes transforms and other transforms of Fourier type
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35K05 Heat equation
41A30 Approximation by other special function classes
41A50 Best approximation, Chebyshev systems
42A10 Trigonometric approximation
49-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to calculus of variations and optimal control
49N45 Inverse problems in optimal control
62D10 Missing data
68Q25 Analysis of algorithms and problem complexity
93E10 Estimation and detection in stochastic control theory
00A15 Bibliographies for mathematics in general
26-01 Introductory exposition (textbooks, tutorial papers, etc.) pertaining to real functions
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References:

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