Glazman-Krein-Naimark theory, left-definite theory, and the square of the Legendre polynomials differential operator.
| dc.contributor.advisor | Littlejohn, Lance, 1951- | |
| dc.creator | Wicks, Quinn Callahan, 1984- | |
| dc.date.accessioned | 2016-07-08T12:48:10Z | |
| dc.date.available | 2016-07-08T12:48:10Z | |
| dc.date.created | 2016-05 | |
| dc.date.issued | 2016-02-27 | |
| dc.date.submitted | May 2016 | |
| dc.date.updated | 2016-07-08T12:48:10Z | |
| dc.description.abstract | As an application of a general left-definite spectral theory, Everitt, Littlejohn and Wellman, in 2002, developed the left-definite theory associated with the classical Legendre self-adjoint second-order differential operator A in L² (−1, 1) which has the Legendre polynomials {Pn} ∞ n=0 as eigenfunctions. As a consequence, they explicitly determined the domain D(A2) of the self-adjoint operator A2 . However, this domain, in their characterization, does not contain boundary conditions in its formulation. In fact, this is a general feature of the left-definite approach developed by Littlejohn and Wellman. Yet, the square of the second-order Legendre expression is in the limit-4 case at each endpoint x = ±1 in L2 (−1, 1), so D(A2) should exhibit four boundary conditions. In this thesis, we show that this domain can, in fact, be expressed using four separated boundary conditions using the classical GKN (Glazman-Krein-Naimark) theory. In addition, we determine a new characterization of D(A2) that involves four non-GKN boundary conditions. These new boundary conditions are surprisingly simple and natural, and are equivalent to the boundary conditions obtained from the GKN theory. | |
| dc.format.mimetype | application/pdf | |
| dc.identifier.uri | http://hdl.handle.net/2104/9654 | |
| dc.language.iso | en | |
| dc.rights.accessrights | Worldwide access. | |
| dc.rights.accessrights | Access changed 7/12/18. | |
| dc.subject | Left-definite theory. Glazman-Krein-Naimark theory. Legendre differential equation. | |
| dc.title | Glazman-Krein-Naimark theory, left-definite theory, and the square of the Legendre polynomials differential operator. | |
| dc.type | Thesis | |
| dc.type.material | text | |
| local.embargo.lift | 2018-05-01 | |
| local.embargo.terms | 2018-05-01 | |
| thesis.degree.department | Baylor University. Dept. of Mathematics. | |
| thesis.degree.grantor | Baylor University | |
| thesis.degree.level | Doctoral | |
| thesis.degree.name | Ph.D. |
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