Function-Theoretic and Probabilistic Approaches to the Problem of Recovering Functions from Korobov Classes in the Lebesgue Metric

Aksaule Zh. Zhubanysheva, Galiya E. Taugynbayeva (), Nurlan Zh. Nauryzbayev, Anar A. Shomanova and Alibek T. Apenov
Additional contact information
Aksaule Zh. Zhubanysheva: Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Satpayev Str., 2, Astana 010008, Kazakhstan
Galiya E. Taugynbayeva: Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Satpayev Str., 2, Astana 010008, Kazakhstan
Nurlan Zh. Nauryzbayev: Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Satpayev Str., 2, Astana 010008, Kazakhstan
Anar A. Shomanova: Faculty of Mechanics and Mathematics, L.N. Gumilyov Eurasian National University, Satpayev Str., 2, Astana 010008, Kazakhstan
Alibek T. Apenov: “Nazarbayev Intellectual School of Science and Mathematics in Nura District of Astana”, Branch of Autonomous Educational Organization “Nazarbayev Intellectual Schools”, Hussein ben Talal Str., 21, Astana 010000, Kazakhstan

Mathematics, 2025, vol. 13, issue 21, 1-20

Abstract: In this article, function-theoretic and probabilistic approaches to the recovery of functions from Korobov classes in Lebesgue metrics are considered. Exact order estimates are obtained for the recovery errors of functions reconstructed from both accurate and inaccurate information given by the trigonometric Fourier–Lebesgue coefficients of the recovered function in the uniform metric. Within these settings, optimal computational aggregates (optimal recovery methods) are constructed. The boundary of inaccurate information (the limiting error ε ˜ N ) that preserves the order of recovery corresponding to accurate information is identified. Furthermore, a set of computational aggregates is constructed whose limiting errors do not exceed ε ˜ N . A procedure for constructing a probability measure on functional classes is presented, and upper bounds for the mean-square recovery error with respect to these measures on Korobov classes are established. Numerical experiments were conducted to validate the theoretical results. These experiments showed that for the function corresponding to the lower bound in Theorem 1 (cases C(N)D-2 and C(N)D-3), the ratio between the function value and the approximation error remains constant in the case of uniform weighting and increases indefinitely when logarithmic weighting is used as the number of terms N grows.

Keywords: recovery functions; function-theoretic approach; probabilistic approach; Korobov classes; accurate information; inaccurate information; limiting error of inaccurate information; measures on functional classes (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/21/3363/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/21/3363/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:21:p:3363-:d:1776977

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().