Baylor University.
The sixth-order Krall differential expression and self-adjoint operators.
Abstract
dc:description.abstractWe first provide an overview of classical GNK Theory for symmetric, or symmatrizable, differential expressions in L2((a, b);w). Then we review how this theory was applied to find a self-adjoint operator in L2 \mu(-1, 1) generated by the sixth-order Lagrangian symmetric Krall differential equation, as done by S. M. Loveland. We later construct the self-adjoint operator generated by the Krall differential equation in the extended Hilbert space L2(-1, 1) + C2 which has the Krall polynomials as (orthogonal) eigenfunctions. The theory we use to create this self-adjoint operator was developed recently by L. L. Littlejohn and R. Wellman as an application of the general Glazman-Krein-Naimark (GKN) Theorem discovered by W. N. Everitt and L. Markus using complex symplectic geometry. In order to explicitly construct this self-adjoint operator, we use properties of functions in the maximal domain in L2(-1, 1) of the Krall expression. As we will see, continuity, as a boundary condition, is forced by our construction of this self-adjoint operator. We also construct six additional examples of self-adjoint operators in an extended Hilbert space, three with a one-dimensional extension space and three with a two-dimensional extension space.
Degree
thesis:*- Name thesis:degree_name
- Ph.D.
- Level thesis:degree_level
- Doctoral
- Grantor
- Baylor University.
- Year dc:date.issued
- 2019
Author and committee
dc:creator, dc:contributor.*- Author dc:creator
-
- Elliott, Katie, 1991-
- Advisor dc:contributor.advisor
-
- Littlejohn, Lance, 1951-
Subjects
dc:subject × 3Rights
dc:rights- Statement dc:rights
-
- Baylor University works are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. Contact libraryquestions@baylor.edu for inquiries about permission.
- Language dc:language.iso
- en
Identifiers
dc:identifier.*- Handle dc:identifier.uri
- https://hdl.handle.net/2104/10658
- OAI identifier oai:identifier
- oai:baylor-ir.tdl.org:2104/10658