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Integral Representations of Positive Linear Functionals
| 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 |
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| 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. |
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| 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 |
