The Nevai condition

Jonathan Breuer, Yoram Last, Barry Simon*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


We study Nevai's condition that for orthogonal polynomials on the real line, Kn(x, x0)2 Kn(x0, x0)-1 dρ(x) → ρx0 Where Kn is the Christoffel-Darboux kernel. We prove that it holds for the Nevai class of a finite gap set uniformly on the spectrum, and we provide an example of a regular measure on [-2,2] where it fails on an interval.

Original languageAmerican English
Pages (from-to)221-254
Number of pages34
JournalConstructive Approximation
Issue number2
StatePublished - 2010

Bibliographical note

Funding Information:
Research of the second author was supported in part by The Israel Science Foundation (Grant No. 1169/06) and Grant No. 2006483 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel.


  • CD kernel
  • Orthogonal polynomials
  • Regular measures


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