Orthogonal polynomials for general measures-I

  • Joseph L. Ullman
Orthogonal Polynomials

DOI: 10.1007/BFb0072438

Part of the Lecture Notes in Mathematics book series (LNM, volume 1105)
Cite this paper as:
Ullman J.L. (1984) Orthogonal polynomials for general measures-I. In: Graves-Morris P.R., Saff E.B., Varga R.S. (eds) Rational Approximation and Interpolation. Lecture Notes in Mathematics, vol 1105. Springer, Berlin, Heidelberg

Abstract

Associated with a unit Borel measure in the complex plane, α, whose support K(α) is compact and contains infinitely many points is a family of orthonormal polynomials {φn(z)}, n=0,1,… . The family of potentials ωn(z)=1 / n log|φn(z)| will be studied. Conditions have previously been found which insure that ωn(z) behaves like the Green's function of O(K(α)), the unbounded component of the complement of K(α). We study the behavior of ωn(z) when these conditions are not satisfied.

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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Joseph L. Ullman
    • 1
  1. 1.Department of MathematicsUniversity of MichiganAnn Arbor

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