Spectra of generators of hyperbolic composition and weighted composition semigroups

TL;DR

This paper characterizes the spectral properties of generators of weighted composition semigroups induced by hyperbolic semiflows on Bergman spaces, highlighting the influence of semigroup behavior near non-fixed points.

Contribution

It provides explicit spectral characterizations for these generators and demonstrates how semigroup behavior near non-fixed points affects spectral properties.

Findings

Complete spectral characterizations for generators of hyperbolic composition semigroups.

Explicit example showing influence of behavior near non-fixed points.

Spectral properties depend on semigroup dynamics near self-contact points.

Abstract

In this paper, we provide complete characterizations for the spectrum, essential spectrum, and point spectrum of the generators of weighted composition $C_0$-semigroups induced by hyperbolic semiflows on Bergman spaces. We give an explicit example showing that the spectral properties can be influenced by the behavior of the semigroup near non-fixed self-contact points.