Lukić, Milivoje2023-08-092023-08-092023-052023-04-04May 2023Gwaltney, Ethan. "Stahl-Totik regularity and exotic spectra of Dirac operators." (2023) Diss., Rice University. <a href="https://hdl.handle.net/1911/115100">https://hdl.handle.net/1911/115100</a>.https://hdl.handle.net/1911/115100This thesis motivates and presents three novel results in the spectral theory of one-dimensional Dirac operators, each of which concerns various forms of exotic or distinguished spectral characteristics. First, we consider the possibility of embedded eigenvalues in the absolutely continuous spectrum of a Dirac operator with operator data of Wigner-von Neumann type. Second, we demonstrate the genericity of Cantor spectrum when the operator data is chosen to be limit-periodic. Third, we provide for the Dirac operator setting an analogue of Stahl-Totik regularity, which, among other things, provides a lower bound on the thickness of the spectrum in terms of the operator data when the data is taken to be uniformly locally square integrable.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 theoryDirac operatorembedded eigenvalueCantor spectrumStahl-Totik regularityThesis2023-08-09