Vague convergence of spectral shift functions for periodic restrictions of one-dimensional Schrodinger operators

We prove weak and vague convergence results for spectral shift functions associated with self-adjoint one-dimensional Schr\"odinger operators on intervals of the form $(-\ell,\ell)$ with periodic boundary conditions to the full-line spectral shift function in the infinite volume limit $\ell\to \infty$. The approach employed relies on the use of a Krein-type resolvent identity to relate the resolvent of the operator with periodic boundary conditions to the corresponding operator with Dirichlet boundary conditions in combination with various operator theoretic facts.

Grantor dc:publisher

University of Tennessee at Chattanooga

Author dc:creator

• Murphy, John B.

Contributors dc:contributor

• Nichols, Roger
• Barioli, Francesco; van der Merwe, Lucas; Wang, Jin
• College of Arts and Sciences

• Schrödinger operator
• Operator theory

Licence

• https://rightsstatements.org/page/InC/1.0/?language=en

Language dc:language

English, eng

Repository record dc:identifier

https://scholar.utc.edu/theses/486

OAI identifier oai:identifier

oai:scholar.utc.edu:theses-1631