Optimal recovery of functions determined by second-order differential operators
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912654060158976 |
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| author | Ling, Bo Gu, Yi |
| author_facet | Ling, Bo Gu, Yi |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_15277 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Optimal recovery of functions determined by second-order differential operators Ling, Bo Gu, Yi Functional Analysis Classical Analysis and ODEs 41A44, 41A25, 47A58, 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. |
| title | Optimal recovery of functions determined by second-order differential operators |
| topic | Functional Analysis Classical Analysis and ODEs 41A44, 41A25, 47A58, |
| url | https://arxiv.org/abs/2510.15277 |