The left-definite spectral analysis of the legendre type differential equation.

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dc.contributor.advisorLittlejohn, Lance, 1951-
dc.contributor.authorTuncer, Davut.
dc.contributor.departmentMathematics.en
dc.contributor.otherBaylor University. Dept. of Mathematics.en
dc.date.accessioned2010-02-02T20:08:14Z
dc.date.available2010-02-02T20:08:14Z
dc.date.copyright2009-12
dc.date.issued2010-02-02T20:08:14Z
dc.description.abstractLittlejohn and Wellman developed a general abstract left-definite theory for a self-adjoint operator A that is bounded below in a Hilbert space (H,(‧,‧)). More specifically, they construct a continuum of Hilbert spaces {(H_r,(‧,‧)_r)}_r>0 and, for each r>0, a self-adjoint restriction A_r of A in H_r. The Hilbert space H_r is called the rth left-definite Hilbert space associated with the pair (H,A) and the operator A_r is called the rth left-definite operator associated with (H,A). We apply this left-definite theory to the self-adjoint Legendre type differential operator generated by the fourth-order formally symmetric Legendre type differential expression ℓ[y](x):=((1-x²)²y″(x))″-((8+4A(1-x²))y′(x))′ +λy(x), where the numbers A and λ are, respectively, fixed positive and non-negative parameters and where x ∈ (-1,1).en
dc.description.degreePh.D.en
dc.description.statementofresponsibilityby Davut Tuncer.en
dc.format.extent197en
dc.format.extent468861 bytes
dc.format.extent707496 bytes
dc.format.mimetypeapplication/pdf
dc.format.mimetypeapplication/pdf
dc.identifier.urihttp://hdl.handle.net/2104/5538
dc.language.isoenen
dc.rightsBaylor University theses 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 librarywebmaster@baylor.edu for inquiries about permission.en
dc.rights.accessrightsWorldwide access.en
dc.rights.accessrightsAccess changed 3/18/13.
dc.subjectLegendre Type Differential Equation.en
dc.subjectSelf-adjoint Operator Theory.en
dc.subjectSpectral Analysis.en
dc.subjectOrthogonal Polynomials.en
dc.subjectSpecial Functions.en
dc.subjectLegendre Type Orthogonal Polynomials.en
dc.subjectLeft-Definite Theory.en
dc.subjectCombinotorics.en
dc.titleThe left-definite spectral analysis of the legendre type differential equation.en
dc.typeThesisen

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