Optimal recovery of functions determined by second-order differential operators
Functional Analysis
2025-10-20 v1 Classical Analysis and ODEs
Abstract
We study the optimal recovery problem for isotropic functions defined by second-order differential operators using both function and gradient values. We derive the upper bound for n-th optimal error with an explicit constant, which is independent of the specific form of the differential operators. Furthermore, for self-adjoint operators, we obtain asymptotic exact results for the n-th optimal error.
Keywords
Cite
@article{arxiv.2510.15277,
title = {Optimal recovery of functions determined by second-order differential operators},
author = {Bo Ling and Yi Gu},
journal= {arXiv preprint arXiv:2510.15277},
year = {2025}
}
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14 pages