Abstract harmonic analysis
In this dissertation we obtain integral representations for positive linear functionals on commutative algebras with involution and semigroups with involution. We prove Bochner and Plancherel type theorems for representations of positive functionals and show that, under some conditions, the Bochner and Plancherel representations are equivalent. We also consider the extension of positive linear functionals on a Banach algebra into a space of pseudoquotients and give under conditions in which the space of pseudoquotients can be identified with all Radon measures on the structure space. In the final chapter we consider a system of integrated Cauchy functional equations on a semigroup, which generalizes a result of Ressel and offers a different approach to the proof.
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Doctor of Philosophy (Ph.D.)
College of Sciences
Length of Campus-only Access
Doctoral Dissertation (Open Access)
Siple, Angela, "Integral Representations of Positive Linear Functionals" (2015). Electronic Theses and Dissertations. 1178.