BULK UNIVERSALITY AND CLOCK SPACING OF ZEROS FOR ERGODIC JACOBI MATRICES WITH ABSOLUTELY CONTINUOUS SPECTRUM

Artur Avila; Yoram Last; Barry Simon

doi:10.2140/apde.2010.3.81

BULK UNIVERSALITY AND CLOCK SPACING OF ZEROS FOR ERGODIC JACOBI MATRICES WITH ABSOLUTELY CONTINUOUS SPECTRUM

Artur Avila^*, Yoram Last, Barry Simon

^*Corresponding author for this work

Einstein Institute of Mathematics

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

29 Scopus citations

Abstract

By combining ideas of Lubinsky with some soft analysis, we prove that universality and clock behavior of zeros for orthogonal polynomials on the real line in the absolutely continuous spectral region is implied by convergence of ¹_nK_n.(x,x) for the diagonal CD kernel and boundedness of the analog associated to second kind polynomials.

Original language	English
Pages (from-to)	81-108
Number of pages	28
Journal	Analysis and PDE
Volume	3
Issue number	1
DOIs	https://doi.org/10.2140/apde.2010.3.81
State	Published - 2010

Bibliographical note

Publisher Copyright:
© 2010,Analysis and PDE.All Rights Reserved

Keywords

Almost mathieu equation
Clock behavior
Orthogonal polynomials

Access to Document

10.2140/apde.2010.3.81

Cite this

@article{ceee9be63e5c4c2e89b2fa4da4590322,

title = "BULK UNIVERSALITY AND CLOCK SPACING OF ZEROS FOR ERGODIC JACOBI MATRICES WITH ABSOLUTELY CONTINUOUS SPECTRUM",

abstract = "By combining ideas of Lubinsky with some soft analysis, we prove that universality and clock behavior of zeros for orthogonal polynomials on the real line in the absolutely continuous spectral region is implied by convergence of 1nKn.(x,x) for the diagonal CD kernel and boundedness of the analog associated to second kind polynomials.",

keywords = "Almost mathieu equation, Clock behavior, Orthogonal polynomials",

author = "Artur Avila and Yoram Last and Barry Simon",

year = "2010",

doi = "10.2140/apde.2010.3.81",

language = "אנגלית",

volume = "3",

pages = "81--108",

journal = "Analysis and PDE",

issn = "2157-5045",

publisher = "Mathematical Sciences Publishers",

number = "1",

}

TY - JOUR

T1 - BULK UNIVERSALITY AND CLOCK SPACING OF ZEROS FOR ERGODIC JACOBI MATRICES WITH ABSOLUTELY CONTINUOUS SPECTRUM

AU - Avila, Artur

AU - Last, Yoram

AU - Simon, Barry

PY - 2010

Y1 - 2010

N2 - By combining ideas of Lubinsky with some soft analysis, we prove that universality and clock behavior of zeros for orthogonal polynomials on the real line in the absolutely continuous spectral region is implied by convergence of 1nKn.(x,x) for the diagonal CD kernel and boundedness of the analog associated to second kind polynomials.

AB - By combining ideas of Lubinsky with some soft analysis, we prove that universality and clock behavior of zeros for orthogonal polynomials on the real line in the absolutely continuous spectral region is implied by convergence of 1nKn.(x,x) for the diagonal CD kernel and boundedness of the analog associated to second kind polynomials.

KW - Almost mathieu equation

KW - Clock behavior

KW - Orthogonal polynomials

UR - http://www.scopus.com/inward/record.url?scp=85118047701&partnerID=8YFLogxK

U2 - 10.2140/apde.2010.3.81

DO - 10.2140/apde.2010.3.81

M3 - ???researchoutput.researchoutputtypes.contributiontojournal.article???

AN - SCOPUS:85118047701

SN - 2157-5045

VL - 3

SP - 81

EP - 108

JO - Analysis and PDE

JF - Analysis and PDE

IS - 1

ER -

BULK UNIVERSALITY AND CLOCK SPACING OF ZEROS FOR ERGODIC JACOBI MATRICES WITH ABSOLUTELY CONTINUOUS SPECTRUM

Abstract

Bibliographical note

Keywords

Access to Document

Other files and links

Fingerprint

Cite this