On the parametrization of self-adjoint extensions of singular Sturm-Liouville operators

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.

Grantor dc:publisher

University of Tennessee at Chattanooga

Author dc:creator

• Beckler, Caleb

Contributors dc:contributor

• Nichols, Roger
• Kong, Lingju; Çetinkaya, Ayça; Wang, Xiunan
• College of Arts and Sciences

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

Licence

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

Language dc:language

English, eng

Repository record dc:identifier

https://scholar.utc.edu/theses/1056

OAI identifier oai:identifier

oai:scholar.utc.edu:theses-2238