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Sharp Lebesgue constants for bounded cubic interpolation ℒ-splines

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Abstract

We construct the Lebesgue function and find sharp Lebesgue constants for bounded cubic interpolation ℒ-splines with equally spaced interpolation nodes and discontinuities of the second derivative chosen so that the cubic ℒ-splines satisfy a certain extremal property with respect to the functions under interpolation.

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Authors and Affiliations

  1. Institute of Mathematics and Mechanics, Ekaterinburg, Russia

    V. A. Kim

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  1. V. A. Kim
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Correspondence to V. A. Kim.

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Original Russian Text Copyright © 2010 Kim V. A.

The author was supported by the Russian Foundation for Basic Research (Grant 08-01-00320) and the State Maintenance Program for the Leading Scientific Schools of the Russian Federation (Grant NSh-1071.2008.1).

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Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 51, No. 2, pp. 330–342, March–April, 2010.

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Kim, V.A. Sharp Lebesgue constants for bounded cubic interpolation ℒ-splines. Sib Math J 51, 267–276 (2010). https://doi.org/10.1007/s11202-010-0026-3

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  • DOI: https://doi.org/10.1007/s11202-010-0026-3

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