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dc.contributor.advisorFlaschka, Hermannen_US
dc.contributor.authorEl Hadrami, Mohamed Lemine Ould, 1962-
dc.creatorEl Hadrami, Mohamed Lemine Ould, 1962-en_US
dc.date.accessioned2013-05-09T11:35:34Z
dc.date.available2013-05-09T11:35:34Z
dc.date.issued1996en_US
dc.identifier.urihttp://hdl.handle.net/10150/290675
dc.description.abstractIn this dissertation, we identify a subgroup Tˢ of Dˢ(μ), the group of Sobolev symplectomorphisms of CP (n), n = 1,2 that has all the properties of a torus of a compact finite dimensional Lie group. We prove that Tˢ: (1) topologically is a submanifold of Dˢ(μ); (2) algebraically is a maximal abelian subgroup of Dˢ(μ); (3) geometrically is flat and totally geodesic. We also characterize the doubly stochastic operators on measurable spaces and use this result to extend the convexity Theorem of T. Bloch, H. Flaschka and T. Ratiu.
dc.language.isoen_USen_US
dc.publisherThe University of Arizona.en_US
dc.rightsCopyright © is held by the author. Digital access to this material is made possible by the University Libraries, University of Arizona. Further transmission, reproduction or presentation (such as public display or performance) of protected items is prohibited except with permission of the author.en_US
dc.subjectMathematics.en_US
dc.titlePoisson algebras and convexityen_US
dc.typetexten_US
dc.typeDissertation-Reproduction (electronic)en_US
thesis.degree.grantorUniversity of Arizonaen_US
thesis.degree.leveldoctoralen_US
dc.identifier.proquest9720631en_US
thesis.degree.disciplineGraduate Collegeen_US
thesis.degree.disciplineMathematicsen_US
thesis.degree.namePh.D.en_US
dc.description.noteThis item was digitized from a paper original and/or a microfilm copy. If you need higher-resolution images for any content in this item, please contact us at repository@u.library.arizona.edu.
dc.identifier.bibrecord.b34548610en_US
dc.description.admin-noteOriginal file replaced with corrected file October 2023.
refterms.dateFOA2018-08-29T21:18:27Z
html.description.abstractIn this dissertation, we identify a subgroup Tˢ of Dˢ(μ), the group of Sobolev symplectomorphisms of CP (n), n = 1,2 that has all the properties of a torus of a compact finite dimensional Lie group. We prove that Tˢ: (1) topologically is a submanifold of Dˢ(μ); (2) algebraically is a maximal abelian subgroup of Dˢ(μ); (3) geometrically is flat and totally geodesic. We also characterize the doubly stochastic operators on measurable spaces and use this result to extend the convexity Theorem of T. Bloch, H. Flaschka and T. Ratiu.


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