3. Electronic Theses and Dissertations (ETDs) - All submissions

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Forward and inverse problem of Hermitian systems in C2.
(2015-05-06) Roth, Thomas
In this thesis, the forward and inverse Spectral Theory for first order Hermitian systems with complex potentials and periodic boundary conditions are studied. The aim of this work is to prove two inverse periodicity Theorems and two uniqueness results for determinants of quasiperiodic boundary value problems.
Geometric and function analytic approaches to the study of Sturm-Liouville theory
(2012-07-04) Roth, Thomas
Ordinary second order linear di erential boundary value problems are of great interest in the study of physical systems, despite this and the length of their history they have many aspects which have only recently been understood. The aim of this work is to examine the geometric and functional analytical approaches to the study of Sturm-Liouville eigenvalue problem with separated boundary conditions. In particular, the following sub-problems will be investigated: Self-adjointness, oscillation theory, variational formulations and the completeness of eigenfunction expansions. The construction of Self-adjoint operators will be studies through de ciency indicies and through symplectic geometry. After the classical variational problem is identi- ed and studied, Lusternik-Schnirelmann theory which is a topologically invariant variational principle will be examined