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Integral Equations and Operator Theory

, Volume 37, Issue 4, pp 397–401 | Cite as

On a Toeplitz determinant identity of Borodin and Okounkov

  • Estelle L. Basor
  • Harold Widom
Article

Abstract

In this note we give two other proofs of an identity of A. Borodin and A. Okounkov which expresses a Toeplitz determinant in terms of the Fredholm determinant of a product of two Hankel operators. The second of these proofs yields a generalization of the identity to the case of block Toeplitz determinants.

AMS Subject Classification

47B35 

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References

  1. [1] E. Basor and J. W. Helton,A new proof of the Szegö limit theorem and new results for Toeplitz operators with discontinuous symbol, J. Operator Th.3 (1980) 23–39.Google Scholar
  2. [2] A. Borodin and A. Okounkov,A Fredholm determinant formula for Toeplitz determinants, preprint, math.CA/9907165.Google Scholar
  3. [3] A. Böttcher and B. Silbermann, Analysis of Toeplitz Operators, Akademie-Verlag, Berlin, 1989.Google Scholar
  4. [4] H. Widom,Toeplitz determinants with singular generating functions, Amer. J. Math.95 (1973) 333–383.Google Scholar
  5. [5] H. Widom,Asymptotic behavior of block Toeplitz matrices and determinants II, Adv. Math.21 (1976) 1–29.Google Scholar

Copyright information

© Birkhäuser Verlag 2000

Authors and Affiliations

  • Estelle L. Basor
    • 1
    • 2
  • Harold Widom
    • 1
    • 2
  1. 1.Department of MathematicsCalifornia Polytechnic State UniversitySan Luis ObispoUSA
  2. 2.Department of MathematicsUniversity of CaliforniaSanta CruzUSA

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