Composition operators on the discrete analogue of generalized Hardy space on homogenous trees

TL;DR

This paper investigates the properties of composition operators on a discrete generalized Hardy space defined on homogeneous trees, focusing on boundedness, compactness, and operator norms induced by automorphisms.

Contribution

It provides new insights into the boundedness, compactness, and norm calculations of composition operators on Hardy spaces over homogeneous trees, a less-explored discrete setting.

Findings

Characterization of boundedness and compactness of composition operators

Explicit computation of operator norms for automorphism-induced symbols

Extension of Hardy space theory to discrete homogeneous tree structures

Abstract

In this paper, we study the basic properties such as boundedness and compactness of composition operators on discrete analogue of generalized Hardy space defined on a homogeneous rooted tree. Also, we compute the operator norm of composition operator when inducing symbol is automorphism of a homogenous tree.