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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 …
Unions Of Lebesgue Spaces And A1 Majorants, Greg Knese, John E. Mccarthy, Kabe Moen
Unions Of Lebesgue Spaces And A1 Majorants, Greg Knese, John E. Mccarthy, Kabe Moen
Mathematics Faculty Publications
We study two questions. When does a function belong to the union of Lebesgue spaces, and when does a function have an A1 majorant? We provide a systematic study of these questions and show that they are fundamentally related. We show that the union ofLwp(ℝn)spaces withw∈Apis equal to the union of all Banach function spaces for which the Hardy–Littlewood maximal function is bounded on the space itself and its associate space.
Introduction To Model Spaces And Their Operators, William T. Ross, Stephan Ramon Garcia, Javad Mashreghi
Introduction To Model Spaces And Their Operators, William T. Ross, Stephan Ramon Garcia, Javad Mashreghi
Bookshelf
The study of model spaces, the closed invariant subspaces of the backward shift operator, is a vast area of research with connections to complex analysis, operator theory and functional analysis. This self-contained text is the ideal introduction for newcomers to the field. It sets out the basic ideas and quickly takes the reader through the history of the subject before ending up at the frontier of mathematical analysis. Open questions point to potential areas of future research, offering plenty of inspiration to graduate students wishing to advance further.