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Nonlinear interpolation and norm minimization

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Abstract

We prove that the set of convolution-type functions in ℝ d that satisfy the interpolation conditions contains a unique function whose convolution element has the minimumL p -norm. The extremal function is determined by solving a nonlinear interpolation problem. The results are applied to an operator recovery problem.

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Authors and Affiliations

  1. Kazakh State University, USSR

    A. A. Zhensykbaev

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  1. A. A. Zhensykbaev
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Translated fromMatematicheskie Zametki, Vol. 58, No. 4, pp. 512–524, October, 1995.

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Zhensykbaev, A.A. Nonlinear interpolation and norm minimization. Math Notes 58, 1033–1041 (1995). https://doi.org/10.1007/BF02305091

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