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Equilibrium measures and capacities in spectral theory. (English) Zbl 1149.31004
The paper constitutes a comprehensive review on the application of potential theory to spectral and inverse spectral theory, mainly to orthogonal polynomials on the real line and on the unit circle. The purposes of the paper are:
1) to explain some of the main aspects of the Stahl-Totik results to spectral theorists,
2) to present the relevant part of Kotani theory to the Orthogonal Polynomial community.
Several open questions are posed and conjectures are made. Extended bibliography on subject is given.

MSC:
31A15 Potentials and capacity, harmonic measure, extremal length and related notions in two dimensions
30C10 Polynomials and rational functions of one complex variable
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