BIT Numerical Mathematics

, Volume 39, Issue 3, pp 439–450

Lacunary Interpolation by Antiperiodic Trigonometric Polynomials

  • Franz-Jürgen Delvos
  • Ludger Knoche

DOI: 10.1023/A:1022314518264

Cite this article as:
Delvos, FJ. & Knoche, L. BIT Numerical Mathematics (1999) 39: 439. doi:10.1023/A:1022314518264


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 

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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