Toeplitzness of composition operators in several variables
Zeljko Cuckovic, Trieu Le
TL;DR
This paper investigates the asymptotic Toeplitzness of composition operators on the Hardy space of the unit sphere in several complex variables, revealing new phenomena in higher dimensions beyond previous one-dimensional results.
Contribution
It extends prior work on Toeplitzness of composition operators from the unit disk to higher-dimensional spheres, uncovering novel behaviors.
Findings
New phenomena in Toeplitzness appear in higher dimensions.
Extended results of Nazarov and Shapiro to C^n.
Identified differences in asymptotic behavior in multiple variables.
Abstract
Motivated by the work of Nazarov and Shapiro on the unit disk, we study asymptotic Toeplitzness of composition operators on the Hardy space of the unit sphere in C^n. We extend some of their results but we also show that new phenomena appear in higher dimensions.
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Taxonomy
TopicsHolomorphic and Operator Theory · Advanced Harmonic Analysis Research · Algebraic and Geometric Analysis