Abstract
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.
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This work was supported by ongoing institutional funding. No additional grants to carry out or direct this particular research were obtained.
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Translated from Sibirskii Matematicheskii Zhurnal, 2024, Vol. 65, No. 2, pp. 235–248. https://doi.org/10.33048/smzh.2024.65.201
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Abramova, E.V., Sivkova, E.O. On the Optimal Recovery of One Family of Operators on a Class of Functions from Approximate Information about Its Spectrum. Sib Math J 65, 245–256 (2024). https://doi.org/10.1134/S0037446624020010
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DOI: https://doi.org/10.1134/S0037446624020010