Cowen, Carl C.Carter, James MichaelKlimek, SlawomirPerez, Rodrigo A.Chin, RaymondBell, Steven R.Mukhin, Evgeny2013-11-062013-11-062013-11-06https://hdl.handle.net/1805/3659http://dx.doi.org/10.7912/C2/2395Indiana University-Purdue University Indianapolis (IUPUI)The main part of this thesis, Chapter 4, contains results on the commutant of a semigroup of operators defined on the Hardy Space of the disk where the operators have hyperbolic non-automorphic symbols. In particular, we show in Chapter 5 that the commutant of the semigroup of operators is in one-to-one correspondence with a Banach algebra of bounded analytic functions on an open half-plane. This algebra of functions is a subalgebra of the standard Newton space. Chapter 4 extends previous work done on maps with interior fixed point to the case of the symbol of the composition operator having a boundary fixed point.en-USComposition operatorCommutantHardy spaceHardy spaces -- ResearchFunctions of complex variablesHilbert spaceOperator theoryFunction spaces -- ResearchBanach algebrasMathematical analysisTopological algebrasComposition operators -- Analysis