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The Bernoulli Spline and Approximation by Trigonometric Blending Polynomials

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Abstract

Using an extension of the notion of Bernoulli spline to a multivariate setting, a Jackson-Favard estimate is derived for approximation of 2π-periodic test functions by trigonometric blending polynomials. Techniques involved in the proof include properties of periodic distributions and of their Fourier transforms. The usual Jackson-Favard estimates from the literature can be derived from our result if limits of test functions are considered.

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Authors and Affiliations

  1. FB Mathematik, Universität Duisburg D —, 4100, Duisburg 1

    Kurt Jetter

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  1. Kurt Jetter
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Dedicated to Professor K. Zeller on occasion of his 65th birthday

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Jetter, K. The Bernoulli Spline and Approximation by Trigonometric Blending Polynomials. Results. Math. 16, 243–252 (1989). https://doi.org/10.1007/BF03322475

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  • DOI: https://doi.org/10.1007/BF03322475

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