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Kernels Of Adjoints Of Composition Operators On Hilbert Spaces Of Analytic Functions, Brittney Rachele Miller
Kernels Of Adjoints Of Composition Operators On Hilbert Spaces Of Analytic Functions, Brittney Rachele Miller
Open Access Dissertations
This thesis contains a collection of results in the study of the adjoint of a composition operator and its kernel in weighted Hardy spaces, in particular, the classical Hardy, Bergman, and Dirichlet spaces. In 2006, Cowen and Gallardo-Gutiérrez laid the groundwork for an explicit formula for the adjoint of a composition operator with rational symbol acting on the Hardy space, and in 2008, Hammond, Moorhouse, and Robbins established such a formula. In 2014, Goshabulaghi and Vaezi obtained analogous formulas for the adjoint of a composition operator in the Bergman and Dirichlet spaces. While it is known that the kernel of …