Damanik, David2023-08-092023-08-092023-052023-04-19May 2023Wang, 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>.https://hdl.handle.net/1911/115187This 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.application/pdfengCopyright 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.spectral theoryHamiltonian systemWeyl-Titchmarsh theoryinverse spectral theorylimit-periodic operatorThesis2023-08-09