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Strong asymptotics for Lp extremal polynomials (1<p≤∞) associated with weights on [−1, 1]

Part of the Lecture Notes in Mathematics book series (LNM,volume 1287)

Abstract

While Szegö type asymptotics of orthonormal polynomials are classical, there has been a longstanding lack of corresponding results for Lp extremal polynomials, p≠2. In particular, in a 1969 paper, Widom raised the question of p=∞. Here we fill some of the gaps for 1<p≤∞.

AMS (MOS) Classification

  • Primary 41A60
  • 42C05

Key Words and Phrases

  • Extremal polynomials
  • strong or power or Szegö asymptotics

Part time at Dept. of Mathematics, Witwatersrand University, 1 Jan Smuts Avenue, Johannesburg 2001, South Africa.

Research supported, in part, by the National Science Foundation Under Grant DMS-8620098.

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© 1987 Springer-Verlag

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Lubinsky, D.S., Saff, E.B. (1987). Strong asymptotics for Lp extremal polynomials (1<p≤∞) associated with weights on [−1, 1]. In: Saff, E.B. (eds) Approximation Theory, Tampa. Lecture Notes in Mathematics, vol 1287. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078899

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  • DOI: https://doi.org/10.1007/BFb0078899

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18500-0

  • Online ISBN: 978-3-540-47991-8

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