Spectrum of Weighted Composition Operators. Part X. The spectrum and essential spectra of weighted automorphisms of the polydisc algebra

TL;DR

This paper analyzes the spectrum and essential spectra of weighted automorphisms of the polydisc algebra, providing detailed descriptions especially for the case when n=2, advancing understanding of their spectral properties.

Contribution

It offers a comprehensive analysis of the spectra of weighted automorphisms of the polydisc algebra, with detailed results for the two-dimensional case, filling gaps in spectral theory.

Findings

Complete description of spectra for n=2

Detailed spectral analysis of weighted automorphisms

Advances understanding of spectral properties in polydisc algebra

Abstract

We investigate the spectrum and the essential spectra of weighted automorphisms of the polydisc algebra $\mathbb{A}^n$. In the case $n=2$ we provide a detailed and, in most cases, complete description of these spectra.