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Integral Representations of Positive Linear Functionals

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Date Issued:
2015
Abstract/Description:
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.
Title: Integral Representations of Positive Linear Functionals.
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Name(s): Siple, Angela, Author
Mikusinski, Piotr, Committee Chair
Atanasiu, Dragu, Committee CoChair
Dutkay, Dorin, Committee Member
Han, Deguang, Committee Member
Lee, Junho, Committee Member
Brennan, Joseph, Committee Member
Huo, Qun, Committee Member
University of Central Florida, Degree Grantor
Type of Resource: text
Date Issued: 2015
Publisher: University of Central Florida
Language(s): English
Abstract/Description: 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.
Identifier: CFE0005713 (IID), ucf:50144 (fedora)
Note(s): 2015-05-01
Ph.D.
Sciences, Mathematics
Doctoral
This record was generated from author submitted information.
Subject(s): Abstract Harmonic Analysis
Persistent Link to This Record: http://purl.flvc.org/ucf/fd/CFE0005713
Restrictions on Access: public 2015-05-15
Host Institution: UCF

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