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arXiv · 2510.15277

Optimal recovery of functions determined by second-order differential operators

Bo Ling·Yi Gu
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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.

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Bo Ling, Yi Gu. 2025-10-17. Optimal recovery of functions determined by second-order differential operators. https://arxiv.org/abs/2510.15277

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