BIT Numerical Mathematics

, Volume 39, Issue 3, pp 439–450

Lacunary Interpolation by Antiperiodic Trigonometric Polynomials

  • Franz-Jürgen Delvos
  • Ludger Knoche


The problem of lacunary trigonometric interpolation is investigated. Does a trigonometric polynomial T exist which satisfies T(xk) = ak, DmT(xk) = bk, 0 ≤ kn − 1, where xk = kπ/n is a nodal set, ak and bk are prescribed complex numbers, \(D = \frac{d}{{dx}}\) and mN. 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.

Lacunary interpolation trigonometric interpolation antiperiodic trigonometric interpolation 


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  1. 1.
    F.-J. Delvos, Hermite interpolation with trigonometric polynomials, BIT, 33 (1993), pp. 113–123.Google Scholar
  2. 2.
    Liu Yongping, On the trigonometric interpolation and the entire interpolation, Approx. Theory Appl., 6:4 (1990), pp. 85–106.Google Scholar
  3. 3.
    A. Sharma and Sun Xiehua, A 2-periodic trigonometric interpolation problem, Approx. Theory Appl., 8:4 (1992), pp. 1–16.Google Scholar
  4. 4.
    A. Sharma and A. K. Varma, Trigonometric interpolation, Duke Math. J., 32 (1965), pp. 341–357.Google Scholar
  5. 5.
    A. Sharma, J. Szabados, and R. S. Varga, 2-Periodic lacunary trigonometric interpolation: the (0; M) case, in Proc. Conf. Constructive Theory of Functions '87, Varna, Bulgaria, pp. 420–426.Google Scholar

Copyright information

© Swets & Zeitlinger 1999

Authors and Affiliations

  • Franz-Jürgen Delvos
    • 1
  • Ludger Knoche
    • 1
  1. 1.Lehrstuhl für Mathematik IUniversität SiegenSiegenGermany, email:

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