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Some remarks on trigonometric interpolation

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Abstract

The object of this paper is to consider the problem of (0, 1, 2, 4) trigonometric interpolation when nodes are taken to bex kn=(2kπ/n),k=0, 1 …,n−1. Here the interpolatory polynomials are explicitly constructed and the corresponding convergence theorem is proved, which is shown to be best possible in a certain sense. It is interesting to compare these results with those of Saxena [6], where the convergence theorem requires the existence off m (x).

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Authors and Affiliations

  1. University of Florida, Gainesville, U.S.A.

    A. K. Varma

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  1. A. K. Varma
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Additional information

I take this opportunity to express my thanks to Professor P. Turán for some valuable conversation which led to this work. The author is at present a member of the faculty of the Dept. of Mathematics, University of Florida, Gainesville, U.S.A.

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Varma, A.K. Some remarks on trigonometric interpolation. Israel J. Math. 7, 177–185 (1969). https://doi.org/10.1007/BF02771665

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  • DOI: https://doi.org/10.1007/BF02771665

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