# Spectra of composition operators on Paley-Wiener spaces and some consequences

## TL;DR

This paper thoroughly investigates the properties of bounded composition operators on Paley-Wiener spaces, including their spectrum, chaos, and stability, revealing detailed operator behavior in this functional analysis context.

## Contribution

It provides comprehensive characterizations of composition operators on Paley-Wiener spaces regarding compactness, spectrum, chaos, and other dynamical properties, filling gaps in the understanding of these operators.

## Key findings

- Complete characterization of compactness and spectrum
- Identification of conditions for Li-Yorke chaos and positive expansivity
- Results on positive shadowing property and Cesàro boundedness

## Abstract

Bounded composition operators in Paley-Wiener spaces have simple forms, and they are just operators composed through affine mappings of the complex plane. The purpose of this article is to explore some notions about bounded operators and linear dynamics and provide complete answers for composition operators in Paley-Wiener spaces concerning compactness, spectrum, spectral radius, Li-Yorke chaos, positive expansivity, positive shadowing property, and absolute Ces\`aro boundedness.