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Adjoints of Composition Operators with Linear Fractional Symbols on the Dirichlet Space of the Disk or the Ball

  • Caixing GuEmail author
Article
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Abstract

In this paper, we discuss the relationship between the adjoints of linear fractional composition operators with respect to two equivalent norms on the Dirichlet space of the disk or the ball. We give a simple and insightful connection between these two norms using the backward shift and the Volterra integration operator. More explicit formulas for the adjoints of linear factional composition operators on the Dirichlet space of the disk or the ball are obtained.

Keywords

Composition operator Dirichlet space of the disk or ball adjoint formula linear fractional transformation 

Mathematics Subject Classification

47B33 47A05 

Notes

Acknowledgements

We thank Professor Pons for making his papers [24, 26] available to us. We thank Jonathan Shapiro for several helpful discussions.

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Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Department of MathematicsCalifornia Polytechnic State UniversitySan Luis ObispoUSA

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