Spectra of Composition Operators on the Unit Ball in Two Complex Variables
Abstract
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 Arveson 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.
Degree
Ph.D.
Advisors
Roeder, Purdue University.
Subject Area
Mathematics
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