Skip to main content
SpringerLink
Log in

Asymptotic behavior of the Christoffel function related to a certain unbounded set

  • Conference paper
  • First Online:
Approximation Theory, Tampa

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

Abstract

We study the asymptotic behavior, as the degree approaches infinity, of the Christoffel function at a fixed point z corresponding to a weight function of the type exp(−|z|λ) on the set |arg z|=π/2+α. The method generalizes that of Rakhmanov and also Mhaskar and Saff.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Landkof, N.S., (1972): Foundations of Modern Potential Theory. Berlin: Springer-Verlag.

    Book  MATH  Google Scholar 

  2. Luo, L.S. and J. Nuttall, (1986): Approximation theory and calculation of energies from divergent perturbation series. Phys. Rev. Lett., 57, 2241–2243.

    Article  Google Scholar 

  3. Mhaskar, H.N., E.B. Saff, (1984): Extremal problems for polynomials with exponential weights. Trans.Amer. Math. Soc. 285, 203–234.

    Article  MATH  MathSciNet  Google Scholar 

  4. Mhaskar, H.N., E.B. Saff, (1985): Where does the sup norm of a weighted polynomial live? Constr. Approx. 1: 71–91.

    Article  MATH  MathSciNet  Google Scholar 

  5. Moretti, G., (1964): Functions of a Complex Variable. Englewood Cliffs, N.J.: Prentice-Hall.

    Google Scholar 

  6. Muskhelishvili, N.I., (1953): Singular Integral Equations. Groningen: Noordhoff.

    MATH  Google Scholar 

  7. Nevai, P.: Geza Freud: Christoffel functions and orthogonal polynomials, J. Approx. Theory, 48, 3–167.

    Google Scholar 

  8. Rakhmanov, E.A., (1984): Asymptotic properties of polynomials orthogonal on the real axis. Math. U.S.S.R. Sbornik, 47, 155–193.

    Article  MATH  MathSciNet  Google Scholar 

  9. Szegö, G., (1975): Orthogonal Polynomials, Amer. Math. Soc. Colloq. Pub, Vol. 23, Providence: American Mathematical Society.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, The University of Western Ontario, N6A 3K7, London, Ontario, Canada

    L. S. Luo & J. Nuttall

Authors
  1. L. S. Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. J. Nuttall
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Edward B. Saff

Rights and permissions

Reprints and permissions

Copyright information

© 1987 Springer-Verlag

About this paper

Cite this paper

Luo, L.S., Nuttall, J. (1987). Asymptotic behavior of the Christoffel function related to a certain unbounded set. In: Saff, E.B. (eds) Approximation Theory, Tampa. Lecture Notes in Mathematics, vol 1287. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078900

Download citation

  • DOI: https://doi.org/10.1007/BFb0078900

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18500-0

  • Online ISBN: 978-3-540-47991-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation