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First-order Trace Formulae for the Iterates of the Fox–Li Operator

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A Panorama of Modern Operator Theory and Related Topics

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 218))

Abstract

The paper is devoted to first-order trace formulas for the iterates of the Fox–Li and related Wiener–Hopf integral operators. Such formulas provide first insight into the asymptotic behaviour of the eigenvalues and can be used to test whether a specific guess for the eigenvalue distribution is acceptable or not. The main technical problem consists in obtaining the asymptotics of a multivariate oscillatory integral whose stationary points constitute a line.

Mathematics Subject Classification (2000). Primary 47B35; Secondary 45C05, 47B10, 78A60.

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Author information

Authors and Affiliations

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

    Albrecht Böttcher

  2. Departamento de Matemáticas, CINVESTAV del I.P.N., 14-740, 07000, Ciudad de México, México

    Sergei Grudsky

  3. Departement Computerwetenschappen, Katholieke Universiteit Leuven, Celestijnenlaan 200A, B-3001, Leuven, Belgium

    Daan Huybrechs

  4. Department of Applied Mathematics and Theoretical Physics Centre for Mathematical Sciences, University of Cambridge, Cambridge, CB3 0WA, UK

    Arieh Iserles

Authors
  1. Albrecht Böttcher
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  2. Sergei Grudsky
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  3. Daan Huybrechs
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  4. Arieh Iserles
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Corresponding author

Correspondence to Albrecht Böttcher .

Editor information

Editors and Affiliations

  1. Dept. Mathematics, Weizmann Institute of Science, Rehovot, Israel

    Harry Dym

  2. Dept. Mathematics &, Computer Sciences, Free University Amsterdam, De Boelelaan 1081 A, Amsterdam, 1081 HV, Netherlands

    Marinus A. Kaashoek

  3. Dept. Mathematics & Statistics, University of Calgary, University Drive NW 2500, Calgary, T2N 1N4, Alberta, Canada

    Peter Lancaster

  4. Inst. Analysis und Scientific Computing, TU Wien, Wiedner Hauptstr. 8-10, Wien, 1040, Austria

    Heinz Langer

  5. Dept. Mathematics, Technion Israel Institute of Technology, Haifa, 32000, Israel

    Leonid Lerer

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Böttcher, A., Grudsky, S., Huybrechs, D., Iserles, A. (2012). First-order Trace Formulae for the Iterates of the Fox–Li Operator. In: Dym, H., Kaashoek, M., Lancaster, P., Langer, H., Lerer, L. (eds) A Panorama of Modern Operator Theory and Related Topics. Operator Theory: Advances and Applications(), vol 218. Springer, Basel. https://doi.org/10.1007/978-3-0348-0221-5_8

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