Boundary uniqueness of harmonic functions and spectral subspaces of operator groups

TL;DR

This paper establishes new uniqueness theorems for harmonic functions and applies these results to characterize spectral subspaces of polynomially bounded operator groups on Banach spaces.

Contribution

It introduces novel uniqueness theorems for harmonic functions and uses them to provide new resolvent descriptions of spectral subspaces in operator theory.

Findings

New uniqueness theorems for harmonic functions on the unit disc and half-plane.

Spectral subspaces characterized via resolvent descriptions.

Applications to polynomially bounded groups of operators.

Abstract

We obtain new uniqueness theorems for harmonic functions defined on the unit disc or in the half plane. These results are applied to obtain new resolvent descriptions of spectral subspaces of polynomially bounded groups of operators on Banach spaces.