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Abstract <p> For a one-parameter family of linear operators, given an operator on a homogeneous Sobolev space with given value of the parameter, we consider the problem of optimal recovery of this operator from incomplete information about this operator with a different value of the parameter. A family of optimal recovery methods is constructed. As a corollary, we obtain optimal methods of recovery of solutions to some equations of mathematical physics. </p>

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Optimal Recovery of Linear Operators on a Homogeneous Sobolev Space

  • 期刊论文

  • 发表日期：

    2025年6月1日

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  • E. O. Sivkova

摘要

Abstract

For a one-parameter family of linear operators, given an operator on a homogeneous Sobolev space with given value of the parameter, we consider the problem of optimal recovery of this operator from incomplete information about this operator with a different value of the parameter. A family of optimal recovery methods is constructed. As a corollary, we obtain optimal methods of recovery of solutions to some equations of mathematical physics.