Spectrum of compact weighted composition operators on the weighted hardy space in the unit ball

Let B(N) be the unit ball in the N-dimensional complex space, for psi, a holomorphic function in B(N), and phi, a holomorphic map from BN into itself, the weighted composition operator on the weighted Hardy space H(2)(beta, B(N)) is given by (C(psi,phi))f =psi(z) f (phi(z)), where f is an element of H(2)(beta, B(N)). This paper discusses the spectrum of C(psi,phi) when it is compact on a certain class of weighted Hardy spaces and when the composition map phi has only one fixed point inside the unit ball. Copyright (c) 2007.