Orthogonal polynomials for general measures-I

  • Joseph L. Ullman
Orthogonal Polynomials
Part of the Lecture Notes in Mathematics book series (LNM, volume 1105)

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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References

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    Widom, Harold, Polynomials associated with measures in the complex plane, Journal of Math. and Mech., Vol. 16, No. 9 (1967) 997–1013.MathSciNetMATHGoogle Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

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

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