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Matematicheskie Zametki, 1995, Volume 58, Issue 4, Pages 512–524 (Mi mzm2072)  
Nonlinear interpolation and norm minimization

A. A. Zhensykbaev

Al-Farabi Kazakh National University
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Abstract: We prove that the set of convolution-type functions in $\mathbb R_d$ that satisfy the interpolation conditions contains a unique function whose convolution element has the minimum $L_p$-norm. The extremal function is determined by solving a nonlinear interpolation problem. The results are applied to an operator recovery problem.
Received: 16.05.1994
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Mathematical Notes, 1995, Volume 58, Issue 4, Pages 1033–1041
DOI: https://doi.org/10.1007/BF02305091
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Language: Russian
Citation: A. A. Zhensykbaev, “Nonlinear interpolation and norm minimization”, Mat. Zametki, 58:4 (1995), 512–524; Math. Notes, 58:4 (1995), 1033–1041
Citation in format AMSBIB
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\by A.~A.~Zhensykbaev
\paper Nonlinear interpolation and norm minimization
\jour Mat. Zametki
\yr 1995
\vol 58
\issue 4
\pages 512--524
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\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=1378332}
\zmath{https://zbmath.org/?q=an:0854.41004}
\transl
\jour Math. Notes
\yr 1995
\vol 58
\issue 4
\pages 1033--1041
\crossref{https://doi.org/10.1007/BF02305091}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=A1995TW84800024}
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