Spectra of linear fractional composition operators on $H^2(B_N)$
Liangying Jiang, Zhihua Chen
TL;DR
This paper characterizes the spectra of linear fractional composition operators on the Hardy space of the unit ball, providing a complete spectral description for all such operators based on their symbol types.
Contribution
It offers a complete spectral characterization of linear fractional composition operators on $H^2(B_N)$, extending previous results to include elliptic and hyperbolic symbols.
Findings
Spectra are fully determined for elliptic and hyperbolic symbols.
The results unify previous partial spectral descriptions.
Complete spectral characterization for all linear fractional composition operators.
Abstract
We characterize the spectra of composition operators on the Hardy space , when the symbols are elliptic or hyperbolic linear fractional self-maps of . Therefore, combining with the result obtained by Bayart \cite{B10}, the spectra of all linear fractional composition operators on are completely determined.
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Taxonomy
TopicsHolomorphic and Operator Theory · Spectral Theory in Mathematical Physics · Advanced Harmonic Analysis Research