Bounds on orthogonal polynomials and separation of their zeros

Eli Levin, Doron S. Lubinsky

Research output: Contribution to journalArticlepeer-review


Let {pn}denote the orthonormal polynomials associated with a measure μ with compact support on the real line. Let μ be regular in the sense of Stahl, Totik, and Ullmann, and I be a subinterval of the support in which μ is absolutely continuous, while μ′ is positive and continuous there. We show that boundedness of the {pn} in that subinterval is closely related to the spacing of zeros of pn and pn-1 in that interval. One ingredient is proving that “local limits” imply universality limits.

Original languageEnglish
Pages (from-to)497-513
Number of pages17
JournalJournal of Spectral Theory
Issue number2
StatePublished - 2022

Bibliographical note

Publisher Copyright:
© 2022 European Mathematical Society Published by EMS Press.


  • Orthogonal polynomials
  • bounds on orthogonal polynomials
  • spacing of zeros


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