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Singular Integral Operators and Related Topics pp 55–118Cite as

Toeplitz Operators with Discontinuous Symbols: Phenomena Beyond Piecewise Continuity

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Part of the book series: Operator Theory Advances and Applications ((OT,volume 90))

Abstract

This paper is a systematic introduction (with a number of new results) to some aspects of the theory of Toeplitz operators with oscillating symbols on the Hardy space H 2 of the unit circle. What we are interested in is obtaining answers to the question which geometric and/or algebraic properties of the argument of the symbol imply that the operator is normally solvable, semi-Fredholm, Fredholm, or even invertible. Our discussion includes well known results on symbols in C + H ∞, SAP, or PQC and also less known and new insights into operators whose streched symbols have arguments behaving like x λ, exp(x λ), (log x)λ, or sin(x λ) with λ > 0 at infinity. We also present some new results on the finite section method for Toeplitz operators.

Research supported by the Alfried Krupp Förderpreis für junge Hochschullehrer of the Krupp Foundation

Research supported by the Deutsche Forschungsgemeinschaft and in part also by the Russian fund of fundamental investigations (Grant 93-011-28)

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Author information

Authors and Affiliations

  1. TU Chemnitz-Zwickau, Fakultät für Mathematik, 09107, Chemnitz, Germany

    Albrecht Böttcher

  2. Faculty of Mechanics and Mathematics, Rostov-on-Don State University, Ul. Bolshaya Sadovaya 105, 344 711, Rostov-on-Don, Russia

    Sergei M. Grudsky

Authors
  1. Albrecht Böttcher
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  2. Sergei M. Grudsky
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Editor information

Editors and Affiliations

  1. School of Mathematical Sciences, Tel-Aviv University, Ramat Aviv, Israel

    I. Gohberg

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© 1996 Birkhäuser Verlag, Basel/Switzerland

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Böttcher, A., Grudsky, S.M. (1996). Toeplitz Operators with Discontinuous Symbols: Phenomena Beyond Piecewise Continuity. In: Böttcher, A., Gohberg, I. (eds) Singular Integral Operators and Related Topics. Operator Theory Advances and Applications, vol 90. Birkhäuser Basel. https://doi.org/10.1007/978-3-0348-9040-3_3

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  • DOI: https://doi.org/10.1007/978-3-0348-9040-3_3

  • Publisher Name: Birkhäuser Basel

  • Print ISBN: 978-3-0348-9881-2

  • Online ISBN: 978-3-0348-9040-3

  • eBook Packages: Springer Book Archive

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