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Approximation Theory, Tampa pp 83–104Cite as

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

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Part of the book series: Lecture Notes in Mathematics ((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≤∞.

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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References

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Author information

Authors and Affiliations

  1. National Research Institute for Mathematical Sciences C.S.I.R., P.O. Box 395, 0001, Pretoria, Rep. of South Africa

    D. S. Lubinsky

  2. Institute for Constructive Mathematics Department of Mathematics, University of South Florida, 33620, Tampa, FL, USA

    E. B. Saff

Authors
  1. D. S. Lubinsky
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  2. E. B. Saff
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Edward B. Saff

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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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