Optimal recovery of integral operators and its applications

2015/09/15 by В. Ф. Бабенко, Yuliya Babenko, Babenko, Vladyslav +5 · 1 citation
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #Mathematical functions and polynomials #Numerical methods in inverse problems

paper · pdf · doi:10.48550/arxiv.1509.04381

openalex publication_date 2015/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we present the solution to the problem of recovering rather arbitrary integral operator based on incomplete information with error. We apply the main result to obtain optimal methods of recovery and compute the optimal error for the solutions to certain integral equations as well as boundary and initial value problems for various PDE's.

Cited by

• Some optimal recovery problems for operators on classes of L-space valued functions

Related

• On optimal recovery of unbounded operators from inaccurate data
• Optimal recovery of linear operators from information of random functions
• Optimal recovery of functions determined by second-order differential operators
• Exact inequalities and optimal recovery by inaccurate information
• On Optimal Recovery of Integrals of Set-Valued Functions