{"id":{"repo_id":"windsor","oai_identifier":"oai:uwindsor.scholaris.ca:20.500.14776/599"},"canonical_url":"https://search.dev.ndltd.org/etd/windsor/oai:uwindsor.scholaris.ca:20.500.14776/599","repository":{"repo_id":"windsor","name":"University of Windsor","base_url":"https://uwindsor.scholaris.ca/server/oai/request"},"display":{"title":"An harmonic analysis for operators on homogeneous Banach spaces.","abstract":"In this thesis, we undertake an harmonic analysis of the Banach algebra L (B) of bounded linear operators on a homogeneous Banach space B of functions on a topological abelian group G. Our analysis is divided into two major parts. In the first, we examine the case where G is compact, particularly G = T (the circle group), and in the second G is locally compact. In both cases, we define the classes of invariant and almost invariant operators in L (B) and investigate their properties. With each T ∈ L (B), we associate a Fourier series and show that this series converges to T in a certain specified sense. For G = T , we show that formal properties of the usual Fourier series hold and also obtain a generalization of the classical F. and M. Riesz theorem for B = CT . For locally compact G, we investigate a subspace of the class of almost invariant operators, namely the almost periodic operators.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2003 .E46. Source: Masters Abstracts International, Volume: 42-02, page: 0601. Adviser: Zhiguo Hu. Thesis (M.Sc.)--University of Windsor (Canada), 2003.","abstract_html":"In this thesis, we undertake an harmonic analysis of the Banach algebra L (B) of bounded linear operators on a homogeneous Banach space B of functions on a topological abelian group G. Our analysis is divided into two major parts. In the first, we examine the case where G is compact, particularly G = T (the circle group), and in the second G is locally compact. In both cases, we define the classes of invariant and almost invariant operators in L (B) and investigate their properties. With each T ∈ L (B), we associate a Fourier series and show that this series converges to T in a certain specified sense. For G = T , we show that formal properties of the usual Fourier series hold and also obtain a generalization of the classical F. and M. Riesz theorem for B = CT . For locally compact G, we investigate a subspace of the class of almost invariant operators, namely the almost periodic operators.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2003 .E46. Source: Masters Abstracts International, Volume: 42-02, page: 0601. Adviser: Zhiguo Hu. Thesis (M.Sc.)--University of Windsor (Canada), 2003.","abstract_has_math":false,"creators":["Emmanuel, Olusakin Joshua."],"institution":"University of Windsor","degree_name":"M.Sc.","degree_level":"Masters","degree_discipline":"Mathematics and Statistics","degree_department":null,"school":null,"contributors":[],"advisors":["Hu, H."],"committee_chairs":[],"committee_members":[],"year":2003,"date_issued":"2003-01-01","date_published":"2003-01-01","updated_at":"2026-07-27T22:04:39Z","subjects":[],"languages":["en_CA"],"rights":[],"rights_urls":["http://creativecommons.org/licenses/by-nc-nd/4.0/"],"identifier_entries":[]},"links":{"outbound_url":"https://hdl.handle.net/20.500.14776/599","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Hu, H."]},{"key":"dc:creator","label":"Author","values":["Emmanuel, Olusakin Joshua."]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2025-06-12 10:59"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2013-03-18 9:54","2025-06-12T14:59:25Z"]},{"key":"dc:date.issued","label":"Date","values":["2003-01-01"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics and Statistics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Masters"]},{"key":"thesis:degree_name","label":"Degree Name","values":["M.Sc."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Windsor"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en_CA"]},{"key":"dc:rights","label":"Dc Rights","values":["http://creativecommons.org/licenses/by-nc-nd/4.0/"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["https://hdl.handle.net/20.500.14776/599"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["In this thesis, we undertake an harmonic analysis of the Banach algebra L (B) of bounded linear operators on a homogeneous Banach space B of functions on a topological abelian group G. Our analysis is divided into two major parts. In the first, we examine the case where G is compact, particularly G = T (the circle group), and in the second G is locally compact. In both cases, we define the classes of invariant and almost invariant operators in L (B) and investigate their properties. With each T ∈ L (B), we associate a Fourier series and show that this series converges to T in a certain specified sense. For G = T , we show that formal properties of the usual Fourier series hold and also obtain a generalization of the classical F. and M. Riesz theorem for B = CT . For locally compact G, we investigate a subspace of the class of almost invariant operators, namely the almost periodic operators.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2003 .E46. Source: Masters Abstracts International, Volume: 42-02, page: 0601. Adviser: Zhiguo Hu. Thesis (M.Sc.)--University of Windsor (Canada), 2003."]},{"key":"dc:title","label":"Title","values":["An harmonic analysis for operators on homogeneous Banach spaces."]}]}],"canonical_facts":{"dc:contributor.advisor":["Hu, H."],"dc:creator":["Emmanuel, Olusakin Joshua."],"dc:date.accessioned":["2025-06-12 10:59"],"dc:date.available":["2013-03-18 9:54","2025-06-12T14:59:25Z"],"dc:date.issued":["2003-01-01"],"dc:description.abstract":["In this thesis, we undertake an harmonic analysis of the Banach algebra L (B) of bounded linear operators on a homogeneous Banach space B of functions on a topological abelian group G. Our analysis is divided into two major parts. In the first, we examine the case where G is compact, particularly G = T (the circle group), and in the second G is locally compact. In both cases, we define the classes of invariant and almost invariant operators in L (B) and investigate their properties. With each T ∈ L (B), we associate a Fourier series and show that this series converges to T in a certain specified sense. For G = T , we show that formal properties of the usual Fourier series hold and also obtain a generalization of the classical F. and M. Riesz theorem for B = CT . For locally compact G, we investigate a subspace of the class of almost invariant operators, namely the almost periodic operators.Dept. of Mathematics and Statistics. Paper copy at Leddy Library: Theses & Major Papers - Basement, West Bldg. / Call Number: Thesis2003 .E46. Source: Masters Abstracts International, Volume: 42-02, page: 0601. Adviser: Zhiguo Hu. 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