Constructive Approximation

, Volume 16, Issue 3, pp 333–357

Problems of Adamjan—Arov—Krein Type on Subsets of the Circle and Minimal Norm Extensions

Authors

  • L. Baratchart
    • INRIA, BP 93, Sophia-Antipolis Cedex
  • J. Leblond
    • INRIA, BP 93, Sophia-Antipolis Cedex
  • J. R. Partington
    • School of Mathematics, University of Leeds
Article

DOI: 10.1007/s003659910015

Cite this article as:
Baratchart, L., Leblond, J. & Partington, J. Constr. Approx. (2000) 16: 333. doi:10.1007/s003659910015

Abstract.

We constructively solve a pair of band-limited generalizations of the Adamjan—Arov—Krein problem. The first one consists in extending a function given on a proper subset of the unit circle to the whole circle so as to make it as close as possible to meromorphic with the prescribed number of poles, in the sup norm, while meeting some gauge constraint. The second consists in directly approximating the given function on the proper subset by the restriction of a meromorphic function, again meeting some gauge constraint.

Key words. Uniform meromorphic approximation, Extremal problems in Hardy spaces, Hankel operators. AMS Classification. 30D55, 30E99, 93B30, 93C80.

Copyright information

© Springer-Verlag New York Inc. 2000