Spectra of Composition Operators on the Unit Ball in Two Complex Variables

2020-06-15T14:42:50Z (GMT) by Michael R Pilla
Let φ be a self-map of B2, the unit ball in C2. We investigate the equation Cφf=λf where we define Cφf : -f◦φ, with f a function in the Drury Arves on Space. After imposing conditions to keep Cφ bounded and well-behaved, we solve the equation Cφf - λf and determine the spectrum σ(Cφ) in the case where there is no interior fixed point and boundary fixed point without multiplicity. We then investigate the existence of one-parameter semigroups for such maps and discuss some generalizations.