On the Dissemination of Results on the Optimal Recovery of Information about the State of the System from Incomplete and Inaccurate Data in the Kiprianov Spaces

DOI: https://doi.org/10.25559/SITITO.020.202403.545-553

Abstract

The results related to the restoration of functions in weight spaces from incomplete spectral data are presented. In this regard, the problem of reconstructing the singular elliptic Laplace - Bessel operator and its degrees of the function from the Fourier - Bessel transformation, given only on some convex set in the dual image space, is considered. The results of the paper are transferring of parts of the results for functions from Sobolev spaces and for the Laplace operator that were previously obtained by G.G. Magaril-Ilyaev, K.Yu. Osipenko and E.O. Sivkova to the case of a singular differential B-elliptic Laplace - Bessel operator (I.A. Kipriyanov's term). The problem of optimal reconstruction of the solution of the Cauchy problem for the singular heat equation with the Bessel operator is also considered. Explicit expressions for the optimal recovery method and its errors are given.

Author Biographies

Alexey Vasilyevich Skrypnikov, Voronezh State University of Engineering Technologies

Head of the Chair of Information Security, Dr. Sci. (Tech.), Associate Professor, Professor

Marina Vasilyevna Polovinkina, Voronezh State University of Engineering Technologies

Head of the Chair of Higher Mathematics, Cand. Sci. (Phys.-Math.), Associate Professor

Igor Petrovich Polovinkin, Voronezh State University; Belgorod State National Research University

Professor of the Chair of Mathematical and Applied Analysis, Applied Mathematics, Informatics and Mechanics Faculty, Dr. Sci. (Phys.-Math.), Associate Professor

Published
2024-10-15
How to Cite
SKRYPNIKOV, Alexey Vasilyevich; POLOVINKINA, Marina Vasilyevna; POLOVINKIN, Igor Petrovich. On the Dissemination of Results on the Optimal Recovery of Information about the State of the System from Incomplete and Inaccurate Data in the Kiprianov Spaces. Modern Information Technologies and IT-Education, [S.l.], v. 20, n. 3, p. 545-553, oct. 2024. ISSN 2411-1473. Available at: <http://sitito.cs.msu.ru/index.php/SITITO/article/view/1147>. Date accessed: 12 sep. 2025. doi: https://doi.org/10.25559/SITITO.020.202403.545-553.
Citation Formats
Issue
Vol 20 No 3 (2024): Modern Information Technologies and IT-education
Section
Theoretical Questions of Computer Science, Computer Mathematics
Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

Publication policy of the journal is based on traditional ethical principles of the Russian scientific periodicals and is built in terms of ethical norms of editors and publishers work stated in Code of Conduct and Best Practice Guidelines for Journal Editors and Code of Conduct for Journal Publishers, developed by the Committee on Publication Ethics (COPE). In the course of publishing editorial board of the journal is led by international rules for copyright protection, statutory regulations of the Russian Federation as well as international standards of publishing. 
Authors publishing articles in this journal agree to the following: They retain copyright and grant the journal right of first publication of the work, which is automatically licensed under the Creative Commons Attribution License (CC BY license). Users can use, reuse and build upon the material published in this journal provided that such uses are fully attributed.