The Nevai condition

Jonathan Breuer; Yoram Last; Barry Simon

doi:10.1007/s00365-009-9055-1

The Nevai condition

Jonathan Breuer, Yoram Last, Barry Simon^*

^*Corresponding author for this work

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

18 Scopus citations

Abstract

We study Nevai's condition that for orthogonal polynomials on the real line, K_n(x, x₀)² K_n(x₀, x₀)^-1 dρ(x) → ρx₀ Where K_n 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 language	English
Pages (from-to)	221-254
Number of pages	34
Journal	Constructive Approximation
Volume	32
Issue number	2
DOIs	https://doi.org/10.1007/s00365-009-9055-1
State	Published - 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.

Keywords

CD kernel
Orthogonal polynomials
Regular measures

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10.1007/s00365-009-9055-1

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title = "The Nevai condition",

abstract = "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.",

keywords = "CD kernel, Orthogonal polynomials, Regular measures",

author = "Jonathan Breuer and Yoram Last and Barry Simon",

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.",

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AU - Simon, Barry

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N2 - 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.

AB - 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.

KW - CD kernel

KW - Orthogonal polynomials

KW - Regular measures

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JO - Constructive Approximation

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IS - 2

ER -

The Nevai condition

Abstract

Bibliographical note

Keywords

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