Thesis.pdf (366.83 kB)

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

Download (366.83 kB)
thesis
posted on 15.06.2020 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.

History

Degree Type

Doctor of Philosophy

Department

Mathematics

Campus location

West Lafayette

Advisor/Supervisor/Committee Chair

Dr. Carl C. Cowen

Additional Committee Member 2

Dr. Rodrigo Pérez

Additional Committee Member 3

Dr. Roland Roeder

Additional Committee Member 4

Dr. Thomas Sinclair

Licence

Exports