Orthogonal Polynomials

Rational Approximation and Interpolation

Volume 1105 of the series Lecture Notes in Mathematics pp 524-528


Orthogonal polynomials for general measures-I

  • Joseph L. UllmanAffiliated withDepartment of Mathematics, University of Michigan

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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.