On the spectrum of multivariable weighted composition operators

In this paper we study the point spectrum of the operator where d ≥ 1, 1 ≤ p ≤ ∞(0, 1] ^d ) and τ is an irrational rotation on 0, 1] ^d . For a particular class of weights w, the point spectrum of T _w,τ is shown to be empty, generalizing Davie’s result 3], who considered the case p = 2, d = 1. Received: 1 June 2007, Revised: 16 October 2007