Study of weighted elliptic composition operators on the unit ball of ℂN

We study the general properties, point spectrum and spectrum of a weighted composition operator Wm,φ{W}_{m,\varphi } with elliptic symbol φ\varphi on the unit ball BN{{\mathbb{B}}}_{N} of CN{{\mathbb{C}}}^{N}, and general weight m∈Hol(BN)m\in {\rm{Hol}}\left({{\mathbb{B}}}_{N}). We give a complete description of the spectra in the majority of cases, and we provide inclusions in general.