Advertisement

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

  • L. S. Luo
  • J. Nuttall
Conference paper
Part of the Lecture Notes in Mathematics book series (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.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Landkof, N.S., (1972): Foundations of Modern Potential Theory. Berlin: Springer-Verlag.CrossRefzbMATHGoogle Scholar
  2. 2.
    Luo, L.S. and J. Nuttall, (1986): Approximation theory and calculation of energies from divergent perturbation series. Phys. Rev. Lett., 57, 2241–2243.CrossRefGoogle Scholar
  3. 3.
    Mhaskar, H.N., E.B. Saff, (1984): Extremal problems for polynomials with exponential weights. Trans.Amer. Math. Soc. 285, 203–234.CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Mhaskar, H.N., E.B. Saff, (1985): Where does the sup norm of a weighted polynomial live? Constr. Approx. 1: 71–91.CrossRefzbMATHMathSciNetGoogle Scholar
  5. 5.
    Moretti, G., (1964): Functions of a Complex Variable. Englewood Cliffs, N.J.: Prentice-Hall.Google Scholar
  6. 6.
    Muskhelishvili, N.I., (1953): Singular Integral Equations. Groningen: Noordhoff.zbMATHGoogle Scholar
  7. 7.
    Nevai, P.: Geza Freud: Christoffel functions and orthogonal polynomials, J. Approx. Theory, 48, 3–167.Google Scholar
  8. 8.
    Rakhmanov, E.A., (1984): Asymptotic properties of polynomials orthogonal on the real axis. Math. U.S.S.R. Sbornik, 47, 155–193.CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Szegö, G., (1975): Orthogonal Polynomials, Amer. Math. Soc. Colloq. Pub, Vol. 23, Providence: American Mathematical Society.Google Scholar

Copyright information

© Springer-Verlag 1987

Authors and Affiliations

  • L. S. Luo
    • 1
  • J. Nuttall
    • 1
  1. 1.Department of PhysicsThe University of Western OntarioLondonCanada

Personalised recommendations