Linear fractional composition operators on weighted Hardy spaces

This thesis consists of two parts. Chapters 2 and 3 comprise the first part. Its foundation is a 1988 paper by Carl Cowen (4). Chapter 4 is the second part. Its motivation is a 1987 paper by Nordgren, Rosenthal and Wintrobe (10).;In his paper, Cowen found a formula expressing the adjoint of any linear fractional composition operator on the Hardy space as a product of Toeplitz operators and another linear fractional composition operator. We build upon this in two different directions.;In chapter 2, a similar formula is obtained for the weighted Bergman spaces. This is used to calculate the norm of any composition operator with affine symbol.;In chapter 3, Cowen's adjoint formula is used to give a unitary equivalence relating composition operators on different weighted Hardy spaces. This result is then applied to some composition operators on the S;In chapter 4, a model is obtained for invertible hyperbolic and parabolic composition operators on H...