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Determinants and Eigenvalues

  • Albrecht Böttcher
  • Bernd Silbermann
Chapter
  • 613 Downloads
Part of the Universitext book series (UTX)

Abstract

We now study the behavior of the determinants
$${D_n}(a): = \det {T_n}(a): = \det \left( {\begin{array}{*{20}{c}} {{a_0}}&{{a_{ - 1}}}& \cdots &{{a_{ - (n - 1)}}} \\ {{a_1}}&{{a_0}}& \cdots &{{a_{ - (n - 2)}}} \\ \vdots & \vdots & \ddots & \vdots \\ {{a_{n - 1}}}&{{a_{n - 2}}}& \cdots &{{a_0}} \end{array}} \right)$$
as n goes to infinity. The strong Szegö limit theorem says that, after appropriate normalization, the determinants Dn(a) approach a nonzero limit provided a is sufficiently smooth and T(a) is invertible. Before stating and proving this theorem, we need a few more auxiliary facts.

Keywords

Toeplitz Operator Trigonometric Polynomial Trace Formula Trace Class Eigenvalue Distribution 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 1999

Authors and Affiliations

  • Albrecht Böttcher
    • 1
  • Bernd Silbermann
    • 1
  1. 1.Fakultät für MathematikTechnische Universität ChemnitzChemnitzGermany

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