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Toeplitz and Singular Integral Operators on General Carleson Jordan Curves

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Singular Integral Operators and Related Topics

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

Abstract

This paper is concerned with the spectra of Toeplitz operators with piecewise continuous symbols and with the symbol calculus for singular integral operators with piecewise continuous coefficients on L P(Γ) where 1 < p < ∞ and Γ is a Carleson Jordan curve. It is well known that piecewise smooth curves lead to the appearance of circular arcs in the essential spectra of Toeplitz operators, and only recently the authors discovered that certain Carleson curves metamorphose these circular arcs into logarithmic double-spirals. In the present paper we dispose of the matter by determining the local spectra produced by a general Carleson curve. These spectra are of a qualitatively new type and may, in particular, be heavy sets — until now such a phenomenon has only be observed for spaces with general Muckenhoupt weights.

Research supported by the Alfried Krupp Förderpreis für junge Hochschullehrer of the Krupp Foundation and in part also by NATO Collaborative Research Grant CRG 950332

Research supported by NATO Collaborative Research Grant CRG 950332

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Author notes

  1. Yu. I. Karlovich

    Present address: Marine Hydrophysical Institute Hydroacoustic Department, Ukrainian Academy of Sciences, Preobrazhenskaya Street 3, 270100, Odessa, Ukraine

Authors and Affiliations

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

    A. Böttcher & Yu. I. Karlovich

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  1. A. Böttcher
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  2. Yu. I. Karlovich
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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., Karlovich, Y.I. (1996). Toeplitz and Singular Integral Operators on General Carleson Jordan Curves. 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_4

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  • DOI: https://doi.org/10.1007/978-3-0348-9040-3_4

  • 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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