Numerical Ranges of Composition Operators with Elliptic Automorphism Symbols

TL;DR

This paper studies the numerical ranges of composition operators with elliptic automorphism symbols of finite order on the Hardy space, providing insights into their spectral properties and geometric structure.

Contribution

It introduces a detailed analysis of the numerical ranges for a specific class of composition operators with elliptic automorphism symbols, expanding understanding in operator theory.

Findings

Characterization of numerical ranges for elliptic automorphism-based composition operators

Identification of geometric properties of these numerical ranges

Connections between automorphism order and numerical range shape

Abstract

In this paper we investigate the numerical ranges of composition operators whose symbols are elliptic automorphisms of finite orders, on the Hilbert Hardy space $H^2(D)$.