Equilibrium Measures and Capacities in Spectral Theory

@inproceedings{Simon2007EquilibriumMA,
  title={Equilibrium Measures and Capacities in Spectral Theory},
  author={Barry Simon},
  year={2007}
}
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 Schrödinger 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… CONTINUE READING
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References

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Showing 1-10 of 104 references

On interpolation

  • P. Erdös, P. Turán
  • III. Interpolatory theory of polynomials, Annals…
  • 1940
Highly Influential
9 Excerpts

On the measure of gaps and spectra for discrete 1D Schrödinger operators

  • Y. Last
  • Comm. Math. Phys. 149
  • 1992
Highly Influential
12 Excerpts

The trace formula for Schrödinger operators on the line

  • W. Craig
  • Comm. Math. Phys. 126
  • 1989
Highly Influential
8 Excerpts

Orthogonal polynomials for general measures

  • J. L. Ullman
  • “Orthogonal Polynomials and Their Applications”
  • 1987
Highly Influential
11 Excerpts

Invariant zero behaviour for orthogonal polynomials on compact sets of the real line

  • W. Van Assche
  • Bull. Soc. Math. Belg. Ser. B 38
  • 1986
Highly Influential
7 Excerpts

Spectral properties of disordered systems in the one-body approximation Comm

  • L. A. Pastur
  • Math. Phys. 75
  • 1980
Highly Influential
6 Excerpts

Electrons in disordered systems and the theory of localization

  • D. J. Thouless
  • Phys. Rep. 13
  • 1974
Highly Influential
7 Excerpts

Localization of eigenstates and transport phenomena in the onedimensional disordered system

  • K. Ishii
  • Supp. Prog. Theor. Phys. 53
  • 1973
Highly Influential
6 Excerpts

Bemerkungen zu einer Arbeit von Herrn M

  • G. Szegő
  • Fekete: Über die Verteilung der Wurzeln bei…
  • 1924
Highly Influential
11 Excerpts

Ergodic Schrödinger Operators (on one foot)

  • S. Jitomirskaya
  • “Spectral Theory and Mathematical Physics: A…
  • 2007
Highly Influential
9 Excerpts

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