{"id":{"repo_id":"ucf","oai_identifier":"oai:stars.library.ucf.edu:etd-2177"},"canonical_url":"https://search.dev.ndltd.org/etd/ucf/oai:stars.library.ucf.edu:etd-2177","repository":{"repo_id":"ucf","name":"Central Florida","base_url":"https://stars.library.ucf.edu/do/oai/"},"display":{"title":"Integral Representations of Positive Linear Functionals","abstract":"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.","abstract_html":"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.","abstract_has_math":false,"creators":["Siple, Angela"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Mikusinski, Piotr"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-01-01T08:00:00Z","date_published":"2015-01-01T08:00:00Z","updated_at":"2026-07-24T05:09:50Z","subjects":["Abstract harmonic analysis","Mathematics"],"languages":["English"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["CFE0005713"],"render_values":[{"text":"CFE0005713","href":null,"code":true}]}]},"links":{"outbound_url":"https://stars.library.ucf.edu/etd/1178","outbound_label":"Repository record","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Mikusinski, Piotr"]},{"key":"dc:creator","label":"Author","values":["Siple, Angela"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:type","label":"Dc Type","values":["Doctoral Dissertation (Open Access)"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Abstract harmonic analysis","Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["English"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["CFE0005713"]},{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://stars.library.ucf.edu/etd/1178"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["<p>If this is your thesis or dissertation, and want to learn how to access it or for more information about readership statistics, contact us at <a href=\"mailto:STARS@ucf.edu\">STARS@ucf.edu</a></p>","Doctor of Philosophy (Ph.D.)","College of Sciences","Mathematics"]},{"key":"dc:description.abstract","label":"Abstract","values":["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."]},{"key":"dc:format","label":"Dc Format","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Integral Representations of Positive Linear Functionals"]}]}],"canonical_facts":{"dc:contributor":["Mikusinski, Piotr"],"dc:creator":["Siple, Angela"],"dc:description":["<p>If this is your thesis or dissertation, and want to learn how to access it or for more information about readership statistics, contact us at <a href=\"mailto:STARS@ucf.edu\">STARS@ucf.edu</a></p>","Doctor of Philosophy (Ph.D.)","College of Sciences","Mathematics"],"dc:description.abstract":["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."],"dc:format":["application/pdf"],"dc:identifier":["CFE0005713"],"dc:identifier.uri":["https://stars.library.ucf.edu/etd/1178"],"dc:language":["English"],"dc:subject":["Abstract harmonic analysis","Mathematics"],"dc:title":["Integral Representations of Positive Linear Functionals"],"dc:type":["Doctoral Dissertation (Open Access)"]},"updated_at":"2026-07-24T05:09:50Z"}