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Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation pp 205–230Cite as

Birkhäuser

Wiener–Hopf Type Operators and Their Generalized Determinants

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Part of the book series: Operator Theory: Advances and Applications ((OT,volume 236))

Abstract

We recall some results on generalized determinants which support a theory of operator τ -functions in the context of their predeterminants which are operators valued in a Banach–Lie group that are derived from the transition maps of certain Banach bundles. Related to this study is a class of Banach–Lie algebras known as L *-algebras from which several results are obtained in relationship to tau functions. We survey the applicability of this theory to that of Schlesinger systems associated with (operator) equations of Fuschsian type and discuss how meromorphic connections may play a role here.

Mathematics Subject Classification (2010). Primary: 47A05, 47B10, 53B10; Secondary: 58B99, 58B25.

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Author information

Authors and Affiliations

  1. Department of Mathematics and Computer Science, Eastern Illinois University, 600 Lincoln Avenue, Charleston, IL, 61920–3099, USA

    James F. Glazebrook

  2. Adjunct Faculty Department of Mathematics, University of Illinois at Urbana–Champaign, Urbana, IL, 61801, USA

    James F. Glazebrook

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  1. James F. Glazebrook
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Correspondence to James F. Glazebrook .

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Editors and Affiliations

  1. Departamento de Análisis Matemático, Universidad de Sevilla, Sevilla, Spain

    Manuel Cepedello Boiso

  2. Department of Mathematics, The Royal Institute of Technology, Stockholm, Sweden

    Håkan Hedenmalm

  3. Department of Mathematics & Computer Sci, Free University Amsterdam, Amsterdam, The Netherlands

    Marinus A. Kaashoek

  4. Departamento de Análisis Matemático, Universidad de Sevilla, Sevilla, Spain

    Alfonso Montes Rodríguez

  5. Department of Mathematics, Brown University, Providence, Rhode Island, USA

    Sergei Treil

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Glazebrook, J.F. (2014). Wiener–Hopf Type Operators and Their Generalized Determinants. In: Cepedello Boiso, M., Hedenmalm, H., Kaashoek, M., Montes Rodríguez, A., Treil, S. (eds) Concrete Operators, Spectral Theory, Operators in Harmonic Analysis and Approximation. Operator Theory: Advances and Applications, vol 236. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-0648-0_13

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