Bounds on orthogonal polynomials and separation of their zeros

  • Eli Levin

    The Open University of Israel, Raanana, Israel
  • Doron S. Lubinsky

    Georgia Institute of Technology, Atlanta, USA
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Abstract

Let denote the orthonormal polynomials associated with a measure with compact support on the real line. Let be regular in the sense of Stahl, Totik, and Ullmann, and be a subinterval of the support in which is absolutely continuous, while is positive and continuous there. We show that boundedness of the in that subinterval is closely related to the spacing of zeros of and in that interval. One ingredient is proving that “local limits” imply universality limits.

Cite this article

Eli Levin, Doron S. Lubinsky, Bounds on orthogonal polynomials and separation of their zeros. J. Spectr. Theory 12 (2022), no. 2, pp. 497–513

DOI 10.4171/JST/408