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<p>We study the optimal recovery problem for isotropic functions defined by second-order differential operators using both function and gradient values. We establish an upper bound for the <i>n</i>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 asymptotically exact results for the <i>n</i>th optimal error.</p>

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Optimal recovery of functions determined by second-order differential operators

  • 期刊论文

  • 发表日期：

    2026年7月27日

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  • Bo Ling,
  • Yi Gu

摘要

We study the optimal recovery problem for isotropic functions defined by second-order differential operators using both function and gradient values. We establish an upper bound for the nth optimal error with an explicit constant, which is independent of the specific form of the differential operators. Furthermore, for self-adjoint operators, we obtain asymptotically exact results for the nth optimal error.