Essential spectra of weighted composition operators induced by elliptic automorphisms

The spectrum of a weighted composition operator C ψ , φ that is induced by an automorphism has been investigated for over 50 years. However, many results are got only under the condition that the weight function ψ is continuous up to the boundary. In this paper we study the spectra and essential spe...

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Bibliographic Details
Published in:Mathematische Zeitschrift 2022-03, Vol.300 (3), p.2333-2348
Main Authors: Dong, Xing-Tang, Gao, Yong-Xin, Zhou, Ze-Hua
Format: Article
Language:English
Subjects:
Automorphisms
Composition
Continuity (mathematics)
Mathematics
Mathematics and Statistics
Operators (mathematics)
Spectra
Weighting functions
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Summary:The spectrum of a weighted composition operator C ψ , φ that is induced by an automorphism has been investigated for over 50 years. However, many results are got only under the condition that the weight function ψ is continuous up to the boundary. In this paper we study the spectra and essential spectra of C ψ , φ on weighted Bergman spaces when φ is an elliptic automorphism, without the assumption that ψ is continuous up to the boundary.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-021-02880-x