Laplacians on Nonisotropic Heisenberg Groups with Multi-Dimensional Center

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dc.contributor.advisorWong, Man Wah
dc.contributor.authorYang, Shengwen
dc.date.accessioned2021-11-15T15:31:36Z
dc.date.available2021-11-15T15:31:36Z
dc.date.copyright2021-07
dc.date.issued2021-11-15
dc.date.updated2021-11-15T15:31:36Z
dc.degree.disciplineMathematics & Statistics
dc.degree.levelDoctoral
dc.degree.namePhD - Doctor of Philosophy
dc.description.abstractWe begin with the construction of the nonisotropic Heisenberg group with multi- dimensional center. The sub-Laplacian on it is introduced. By taking the inverse Fourier transform of the sub-Laplacian with respect to the center, we get a family of twisted Laplacians. They are proved to be globally hypoelliptic in the Schwartz space and in the Gelfand-Shilov spaces using the Green functions of the twisted Laplacians. Global regularity in a scale of Sobolev spaces of these twisted Laplacians is given. Equally important are the heat semigroups generated by the twisted Laplacians in terms of Weyl transforms and the Lp Lq estimates of these heat semigroups are presented. Finally, the eigenvalues and eigenfunctions of the twisted bi-Laplacians on these Heisenberg groups are studied in the context of analytic number theory. Global hypoellipticty, essential self-adjointness, Sobolev spaces as well as the Sobolev estimates of the twisted bi-Laplacians are also introduced.
dc.identifier.urihttp://hdl.handle.net/10315/38716
dc.languageen
dc.rightsAuthor owns copyright, except where explicitly noted. Please contact the author directly with licensing requests.
dc.subject.keywordsMathematics
dc.subject.keywordsHeisenberg Groups
dc.subject.keywordsLaplacians
dc.subject.keywordsTwisted Laplacians
dc.subject.keywordsSub-Laplacians
dc.subject.keywordsHeat Kernels
dc.subject.keywordsGreen Functions
dc.subject.keywordsGlobal Hypoellipticity
dc.subject.keywordsEssential Self-Adjointness
dc.subject.keywordsHeat Semigroups
dc.subject.keywordsTwisted Bi-Laplacian
dc.subject.keywordsSpectral Properties
dc.subject.keywordsGelfand–Shilov Spaces
dc.subject.keywordsSchwartz Space
dc.subject.keywordsSobolev Spaces
dc.subject.keywordsSpectral Analysis
dc.titleLaplacians on Nonisotropic Heisenberg Groups with Multi-Dimensional Center
dc.typeElectronic Thesis or Dissertation

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