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Abstract <p> We solve the problem of recovering the fractional Laplacian on a Sobolev class of functions in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb R^d\)</EquationSource> </InlineEquation> from incomplete information about the functions in this class. Namely, for every function in this class, its Fourier transform on a measurable subset in <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb R^d\)</EquationSource> </InlineEquation> is assumed to be known either exactly or approximately. We also construct a family of linear optimal recovery methods. </p>

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On Optimal Recovery of Fractional Laplacians from Inaccurate Information

  • 期刊论文

  • 发表日期：

    2025年12月1日

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  • G. G. Magaril-Il’yaev,
  • E. O. Sivkova

摘要

Abstract

We solve the problem of recovering the fractional Laplacian on a Sobolev class of functions in \(\mathbb R^d\) from incomplete information about the functions in this class. Namely, for every function in this class, its Fourier transform on a measurable subset in \(\mathbb R^d\) is assumed to be known either exactly or approximately. We also construct a family of linear optimal recovery methods.