BIT Numerical Mathematics

, Volume 39, Issue 3, pp 439–450

Lacunary Interpolation by Antiperiodic Trigonometric Polynomials

  • Franz-Jürgen Delvos
  • Ludger Knoche
Article

Abstract

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 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  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: delvos@mathematik.uni-siegen.de

Personalised recommendations