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Equilibrium measures and capacities in spectral theory

Simon, Barry (2007) Equilibrium measures and capacities in spectral theory. . (Submitted) http://resolver.caltech.edu/CaltechAUTHORS:20170512-091544520

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Abstract

This is a comprehensive review of the uses of potential theory in studying the spectral theory of orthogonal polynomials. Much of the article focuses on the Stahl–Totik theory of regular measures, especially the case of OPRL and OPUC. Links are made to the study of ergodic Schr¨odinger operators where one of our new results implies that, in complete generality, the spectral measure is supported on a set of zero Hausdorff dimension (indeed, of capacity zero) in the region of strictly positive Lyapunov exponent. There are many examples and some new conjectures and indications of new research directions. Included are appendices on potential theory and on Fekete–Szegő theory.


Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription
https://arxiv.org/abs/0711.2700arXivDiscussion Paper
ORCID:
AuthorORCID
Simon, Barry0000-0003-2561-8539
Additional Information:August 23, 2007. (Submitted on 16 Nov 2007) Supported in part by NSF grants DMS-0140592 and DMS-0652919 and U.S.–Israel Binational Science Foundation (BSF) Grant No.2002068.
Funders:
Funding AgencyGrant Number
NSFDMS-0140592
NSFDMS-0652919
Binational Science Foundation (USA-Israel)2002068
Subject Keywords:Potential theory, spectral theory, regular orthogonal polynomials
Classification Code:MSC: Primary: 31A15, 05E35, 34L05. Secondary: 31A35, 33D45, 34P05
Record Number:CaltechAUTHORS:20170512-091544520
Persistent URL:http://resolver.caltech.edu/CaltechAUTHORS:20170512-091544520
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:77394
Collection:CaltechAUTHORS
Deposited By: Ruth Sustaita
Deposited On:12 May 2017 23:45
Last Modified:12 May 2017 23:45

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