Essential Spectra of Weighted Composition Operators Induces by Elliptic Automorphisms

2020/11/30 by Dong, Xing-Tang, Gao, Yong-Xin, Zhou, Ze-Hua · 1 citation
#FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2011.14606

Abstract

The spectrum of a weighted composition operator C_{ψ, φ} who is induced by an automorphism has been investigated for over fifty 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.

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