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On uniform Lebesgue constants of local exponential splines with equidistant knots

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Abstract

For a linear differential operator L r of arbitrary order r with constant coefficients and real pairwise different roots of the characteristic polynomial, we study Lebesgue constants (the norms of linear operators from C to C) of local exponential splines corresponding to this operator with a uniform arrangement of knots; such splines were constructed by the authors in earlier papers. In particular, for the third-order operator L 3 = D(D 2 − β 2) (β > 0), we find the exact values of Lebesgue constants for two types of local splines and compare these values with Lebesgue constants of exponential interpolation splines.

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Authors and Affiliations

  1. Krasovskii Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Yekaterinburg, 620990, Russia

    E. V. Strelkova & V. T. Shevaldin

Authors
  1. E. V. Strelkova
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  2. V. T. Shevaldin
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Correspondence to V. T. Shevaldin.

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Original Russian Text © E.V. Strelkova, V.T. Shevaldin, 2015, published in Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2015, Vol. 21, No. 4.

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Strelkova, E.V., Shevaldin, V.T. On uniform Lebesgue constants of local exponential splines with equidistant knots. Proc. Steklov Inst. Math. 296 (Suppl 1), 206–217 (2017). https://doi.org/10.1134/S0081543817020195

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