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Mathematics > Spectral Theory

arXiv:0711.2700 (math)
[Submitted on 16 Nov 2007]

Title:Equilibrium measures and capacities in spectral theory

Authors:Barry Simon
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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 Schrodinger 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-Szego theory.
Subjects: Spectral Theory (math.SP)
MSC classes: 31A15; 05E35; 34L05
Cite as: arXiv:0711.2700 [math.SP]
  (or arXiv:0711.2700v1 [math.SP] for this version)
  https://doi.org/10.48550/arXiv.0711.2700

Submission history

From: Barry Simon [view email]
[v1] Fri, 16 Nov 2007 23:06:30 UTC (60 KB)
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