Topics in non-locally convex functional analysis and geometrical analysis with applications to boundary value problems
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[ACCESS RESTRICTED TO THE UNIVERSITY OF MISSOURI AT AUTHOR'S REQUEST.] This dissertation is comprised of two parts. The first part, consisting of chapters 2-13, deals with issues pertaining to non-locally functional analysis. Specifically, we generalize the classical trilogy, Open Mapping Theorem, Closed Graph Theorem, and Uniform Boundedness Principle to the setting of quasi-pseudonormed groups via techniques rooted in groupoid metrization theorems. In addition, here we address issues such as completeness, separability, and pointwise convergence in environments which are considerably more general than those in the current literature. In the second part, which is embodied in chapters 14-23, we deal with topics from geometrical analysis and applications to Boundary Value Problems. Concretely, we start by discussing the geometry of pseudo-balls, then proceed to give characterization of Lipschitz domains. This culminates with the formulation and proof of a sharp version of the Boundary Point Principle extending the classical work of E. Hopf and O.A. Oleinik. Finally, the latter is used in the treatment of Boundary Value Problems.
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Access is limited to the campus of the University of Missouri--Columbia.