Spectrum of Compact Weighted Composition Operators on the Weighted Hardy Space in the Unit Ball

Let BN be the unit ball in the N-dimensional complex space, for , a holomorphic function in BN, and , a holomorphic map from BN into itself, the weighted composition operator on the weighted Hardy space H2( 2,BN) is given by (C , )f= (z)f( (z)), where f ￠ H2( 2,BN). This paper discusses the spectrum of C , when it is compact on a certain class of weighted Hardy spaces and when the composition map has only one fixed point inside the unit ball.