On uniform Lebesgue constants of local exponential splines with equidistant knots |
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Authors: | E V Strelkova V T Shevaldin |
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Affiliation: | 1.Krasovskii Institute of Mathematics and Mechanics,Ural Branch of the Russian Academy of Sciences,Yekaterinburg,Russia |
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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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