Analytic structure of weighted shifts on directed trees

TL;DR

This paper explores the connection between weighted shifts on directed trees and multiplier algebras of analytic functions, using this relationship to analyze their spectral properties.

Contribution

It establishes a novel link between weighted shifts on directed trees and multiplier algebras, enabling new spectral analysis methods.

Findings

Weighted shifts are related to multiplier algebras of analytic functions.

Spectral properties of these operators are characterized.

The approach provides new insights into operator theory on directed trees.

Abstract

We show that a weighted shift on a directed tree is related to a multiplier algebra of coefficients of analytic functions. We use this relation to study spectral properties of the operators in question.