The sixth-order Krall differential expression and self-adjoint operators.

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dc.contributor.advisorLittlejohn, Lance, 1951-
dc.creatorElliott, Katie, 1991-
dc.creator.orcid0000-0002-1254-8714
dc.date.accessioned2019-07-29T13:29:12Z
dc.date.available2019-07-29T13:29:12Z
dc.date.created2019-05
dc.date.issued2019-03-22
dc.date.submittedMay 2019
dc.date.updated2019-07-29T13:29:12Z
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.
dc.format.mimetypeapplication/pdf
dc.identifier.urihttps://hdl.handle.net/2104/10658
dc.language.isoen
dc.rights.accessrightsWorldwide access.
dc.rights.accessrightsAccess changed 8/16/21.
dc.subjectSelf-adjoint operators. Krall differential expression. Extended Hilbert space.
dc.titleThe sixth-order Krall differential expression and self-adjoint operators.
dc.typeThesis
dc.type.materialtext
local.embargo.lift2021-05-01
local.embargo.terms2021-05-01
thesis.degree.departmentBaylor University. Dept. of Mathematics.
thesis.degree.grantorBaylor University
thesis.degree.levelDoctoral
thesis.degree.namePh.D.

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