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Lacunary Interpolation by Antiperiodic Trigonometric Polynomials

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Abstract

The problem of lacunary trigonometric interpolation is investigated. Does a trigonometric polynomial T exist which satisfies T(x k) = a k, D m T(x k) = b k, 0 ≤ k ≤ n − 1, where x k = kπ/n is a nodal set, a k and b k are prescribed complex numbers, \(D = \frac{d}{{dx}}\) and m ∈ N. Results obtained by several authors for the periodic case are extended to the antiperiodic case. In particular solvability is established when n as well as m are even. In this case a periodic solution does not exist.

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Authors and Affiliations

  1. Lehrstuhl für Mathematik I, Universität Siegen, 57068, Siegen, Germany, email: delvos@mathematik.uni-siegen.de

    Franz-Jürgen Delvos & Ludger Knoche

Authors
  1. Franz-Jürgen Delvos
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  2. Ludger Knoche
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Delvos, FJ., Knoche, L. Lacunary Interpolation by Antiperiodic Trigonometric Polynomials. BIT Numerical Mathematics 39, 439–450 (1999). https://doi.org/10.1023/A:1022314518264

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  • DOI: https://doi.org/10.1023/A:1022314518264

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