Weighted composition operators on the Fock space: iteration and semigroups

TL;DR

This paper studies the behavior and classification of weighted composition operators on the Fock space, analyzing both discrete powers and continuous semigroups, including their generators and asymptotic properties.

Contribution

It provides a comprehensive classification of continuous semigroups of weighted composition operators on the Fock space and calculates their generators, extending understanding of their dynamics.

Findings

Asymptotic behavior of discrete semigroups analyzed

Full classification of continuous semigroups provided

Generators of semigroups explicitly calculated

Abstract

This paper considers discrete and continuous semigroups of (weighted) composition operators on the Fock space. For discrete semigroups consisting of powers of a single operator, the asymptotic behaviour of the semigroups is analysed. For continuous semigroups and groups, a full classification of possible semigroups is given, and the generator is calculated.