Spectra of linear fractional composition operators on $H^2(B_N)$

Abstract

We characterize the spectra of composition operators on the Hardy space $H^2(B_N)$, when the symbols are elliptic or hyperbolic linear fractional self-maps of $B_N$. Therefore, combining with the result obtained by Bayart \cite{B10}, the spectra of all linear fractional composition operators on $H^2(B_N)$ are completely determined.

22 pages