Committee Chair

Nichols, Roger

Committee Member

Barioli, Francesco; van der Merwe, Lucas; Wang, Jin

Department

Dept. of Mathematics

College

College of Arts and Sciences

Publisher

University of Tennessee at Chattanooga

Place of Publication

Chattanooga (Tenn.)

Abstract

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.

Acknowledgments

I am indebted to my advisor, Roger Nichols, for the help he provided me in completing this thesis. I am extremely lucky to have a professor as patient and knowledgable as he is. I thank my mom, Denise Murphy, for being a great mother. I also thank Doug and Nancy Murphy for believing in me. I also thank my siblings, Ashley and Thomas, for always being there for me. Also, I thank all my friends, family, professors, teachers, and coaches that have made me who I am today. I would like to thank the members of my committee, Drs. Barioli, van der Merwe, and Wang for their advice and encouragement.

Degree

M. S.; A thesis submitted to the faculty of the University of Tennessee at Chattanooga in partial fulfillment of the requirements of the degree of Master of Science.

Date

12-2016

Subject

Schrödinger operator; Operator theory

Keyword

Spectral shift function; Schrodinger operator; Vague convergence; Periodic boundary conditions

Document Type

Masters theses

Extent

vii, 67 leaves

Language

English

Rights

Under copyright.

License

http://creativecommons.org/licenses/by-nd/3.0/

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