Constrained L2-Approximation by Polynomials on Subsets of the Circle

  • Laurent Baratchart
  • Juliette Leblond
  • Fabien Seyfert
Part of the Fields Institute Communications book series (FIC, volume 81)


We study best approximation to a given function, in the least square sense on a subset of the unit circle, by polynomials of given degree which are pointwise bounded on the complementary subset. We show that the solution to this problem, as the degree goes large, converges to the solution of a bounded extremal problem for analytic functions which is instrumental in system identification. We provide a numerical example on real data from a hyperfrequency filter.

2010 Mathematics Subject Classification.

30E10 30E25 41A10 46N10 47A52 93B30 


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Laurent Baratchart
    • 1
  • Juliette Leblond
    • 1
  • Fabien Seyfert
    • 1
  1. 1.INRIASophia-Antipolis CedexFrance

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