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

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dc.contributor.advisor Littlejohn, Lance L. Tuncer, Davut.
dc.contributor.other Baylor University. Dept. of Mathematics. en 2009-12
dc.description.abstract Littlejohn 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.rights Baylor 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 for inquiries about permission. en
dc.subject Legendre Type Differential Equation. en
dc.subject Self-adjoint Operator Theory. en
dc.subject Spectral Analysis. en
dc.subject Orthogonal Polynomials. en
dc.subject Special Functions. en
dc.subject Legendre Type Orthogonal Polynomials. en
dc.subject Left-Definite Theory. en
dc.subject Combinotorics. en
dc.title The left-definite spectral analysis of the legendre type differential equation. en
dc.type Thesis en Ph.D. en
dc.rights.accessrights Worldwide access. en
dc.rights.accessrights Access changed 3/18/13.
dc.contributor.department Mathematics. en

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