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

Let Open image in new window be the unit ball in the Open image in new window -dimensional complex space, for Open image in new window , a holomorphic function in Open image in new window , and Open image in new window , a holomorphic map from Open image in new window into itself, the weighted composition operator on the weighted Hardy space Open image in new window is given by Open image in new window , where Open image in new window . This paper discusses the spectrum of Open image in new window when it is compact on a certain class of weighted Hardy spaces and when the composition map Open image in new window has only one fixed point inside the unit ball.