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Recent Advances in Operator Theory pp 217–241Cite as

Birkhäuser

A Status Report on the Asymptotic Behavior of Toeplitz Determinants with Fisher-Hartwig Singularities

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 124))

Abstract

The Fisher-Hartwig conjecture describes the asymptotic behavior of Toeplitz determinants for a certain class of singular generating functions. It has been proved in many cases and reformulated in others. Recently, the author proved the conjecture in all the cases in which it can be expected to be true. In the present paper we want to give an account of the latest developments in connection with this conjecture and describe the main ideas of the proof.

Dedicated to I. Gohberg on the occasion of his 70-th birthday

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Author information

Authors and Affiliations

  1. Fakultät für Mathematik, Technische Universität Chemnitz, 09107, Chemnitz, Germany

    Torsten Ehrhardt

Authors
  1. Torsten Ehrhardt
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Editor information

Editors and Affiliations

  1. Department of Mathematics, University of Groningen, P.O. Box 800, 9700 AV, Groningen, The Netherlands

    A. Dijksma

  2. Division of Mathematics and Computer Science Faculty of Sciences, Vrije Universiteit, De Boelelaan 1081a, 1081 HV, Amsterdam, The Netherlands

    M. A. Kaashoek  & A. C. M. Ran  & 

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© 2001 Springer Basel AG

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Ehrhardt, T. (2001). A Status Report on the Asymptotic Behavior of Toeplitz Determinants with Fisher-Hartwig Singularities. In: Dijksma, A., Kaashoek, M.A., Ran, A.C.M. (eds) Recent Advances in Operator Theory. Operator Theory: Advances and Applications, vol 124. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8323-8_11

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  • DOI: https://doi.org/10.1007/978-3-0348-8323-8_11

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9516-3

  • Online ISBN: 978-3-0348-8323-8

  • eBook Packages: Springer Book Archive

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