Spectrum of weighted composition operators part X: the spectrum and essential spectra of weighted automorphisms of the polydisc algebra

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