Direct and Inverse Spectral Theory for the Hamiltonian System with Measure Coecients

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dc.contributor.advisorDamanik, Daviden_US
dc.creatorWang, Chunyien_US
dc.date.accessioned2023-08-09T19:20:40Zen_US
dc.date.available2023-08-09T19:20:40Zen_US
dc.date.created2023-05en_US
dc.date.issued2023-04-19en_US
dc.date.submittedMay 2023en_US
dc.date.updated2023-08-09T19:20:40Zen_US
dc.description.abstractThis thesis discusses the direct and inverse spectral theory of Hamiltonian systems with measure coefficients, which can cover more singular cases. In the first part, we define self-adjoint relations associated with the systems and develop Weyl-Titchmarsh theory for these relations. Then, we develop subordinacy theory for the relations and discuss several cases when the absolutely continuous spectrum appears. Finally, we develop inverse uniqueness results for Hamiltonian systems with measure coefficients by applying de Branges’ subspace ordering theorem. Overall, this thesis contributes to the study of Hamiltonian systems with measure coefficients, expands the self-adjoint operator theory to a more general class of physical models, and investigates common spectral properties among different models.en_US
dc.format.mimetypeapplication/pdfen_US
dc.identifier.citationWang, Chunyi. "Direct and Inverse Spectral Theory for the Hamiltonian System with Measure Coecients." (2023) Diss., Rice University. <a href="https://hdl.handle.net/1911/115187">https://hdl.handle.net/1911/115187</a>.en_US
dc.identifier.urihttps://hdl.handle.net/1911/115187en_US
dc.language.isoengen_US
dc.rightsCopyright is held by the author, unless otherwise indicated. Permission to reuse, publish, or reproduce the work beyond the bounds of fair use or other exemptions to copyright law must be obtained from the copyright holder.en_US
dc.subjectspectral theoryen_US
dc.subjectHamiltonian systemen_US
dc.subjectWeyl-Titchmarsh theoryen_US
dc.subjectinverse spectral theoryen_US
dc.subjectlimit-periodic operatoren_US
dc.titleDirect and Inverse Spectral Theory for the Hamiltonian System with Measure Coecientsen_US
dc.typeThesisen_US
dc.type.materialTexten_US
thesis.degree.departmentMathematicsen_US
thesis.degree.disciplineNatural Sciencesen_US
thesis.degree.grantorRice Universityen_US
thesis.degree.levelDoctoralen_US
thesis.degree.nameDoctor of Philosophyen_US
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