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Commuting Toeplitz operators with harmonic symbols

Integral Equations and Operator Theory volume 14, pages 1–12 (1991)Cite this article

Abstract

This paper shows that on the Bergman space, two Toeplitz operators with harmonic symbols commute only in the obvious cases. The main tool is a characterization of harmonic functions by a conformally invariant mean value property.

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References

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Authors and Affiliations

  1. Department of Mathematics, Michigan State University, 48824, East Lansing, MI, USA

    Sheldon Axler & Željko Čučković

  2. Faculty of Technology, University of Zagreb, Pierottijeva 6, Zagreb, Yugoslavia

    Željko Čučković

Authors
  1. Sheldon Axler
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  2. Željko Čučković
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Additional information

The first author was partially supported by the National Science Foundation.

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Axler, S., Čučković, Ž. Commuting Toeplitz operators with harmonic symbols. Integr equ oper theory 14, 1–12 (1991). https://doi.org/10.1007/BF01194925

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  • DOI: https://doi.org/10.1007/BF01194925

Keywords

  • Harmonic Function
  • Main Tool
  • Toeplitz Operator
  • Bergman Space
  • Obvious Case