Committee Chair

Nichols, Roger

Committee Member

Kong, Lingju; Çetinkaya, Ayça; Wang, Xiunan

Department

Dept. of Mathematics

College

College of Arts and Sciences

Publisher

University of Tennessee at Chattanooga

Place of Publication

Chattanooga (Tenn.)

Abstract

The self-adjoint extensions of a lower semi-bounded minimal Sturm–Liouville operator are parametrized using generalized boundary values defined by fixed choices of special nonoscillatory solutions, called principal and nonprincipal solutions. However, principal and nonprincipal solutions are not unique, and different choices yield different generalized boundary values. Therefore, the parametrization of self-adjoint extensions inherently depends upon the choices of principal and nonprincipal solutions. Using known properties of principal and nonprincipal solutions, Wronskian techniques, and the Pl¨ucker identity, we find the relation between self-adjoint extensions for two different parametrizations.

Acknowledgments

I am indebted to my eternally patient thesis advisor Dr. Roger Nichols, thank you so much. Special thanks to the faculty of the Department of Mathematics at The University of Tennessee at Chattanooga for educating me and allowing me to pursue this thesis. Thank you, Deborah Barr, for making the Department of Mathematics a joy to be a part of.

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

5-2026

Subject

Operator theory; Selfadjoint operators; Spectral theory (Mathematics); Sturm-Liouville equation

Keyword

Sturm-Liouville Operator; Self-Adjoint Extensions; Generalized Boundary Values; Plucker Identity

Document Type

Masters theses

DCMI Type

Text

Extent

vii, 31 leaves

Language

English

Rights

http://rightsstatements.org/vocab/InC/1.0/

License

http://creativecommons.org/licenses/by/4.0/

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