Differential operators and the Legendre type polynomials
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Publication:803359
zbMath0727.34021MaRDI QIDQ803359
W. Norrie Everitt, Lance L. Littlejohn
Publication date: 1988
Published in: Differential and Integral Equations (Search for Journal in Brave)
polynomial solutionsfourth-order ordinary differential equationformally symmetric operatorLegendre type polynomialsorthogonality of the derivatives
Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Weyl theory and its generalizations for ordinary differential equations (34B20) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30)
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A general left-definite theory for certain self-adjoint operators with applications to differential equations ⋮ Sampling theorems associated with fourth- and higher-order self-adjoint eigenvalue problems ⋮ Spectral analysis of Legendre type fourth-order operators on the real axis ⋮ Coexistence of analytic and distributional solutions for linear differential equations. I ⋮ An algebraic approach to certain differential eigenvalue problems ⋮ The left-definite Legendre type boundary problem ⋮ A left-definite study of Legendre's differential equation and the fourth-order Legendre type differential equation ⋮ Self-adjoint operators and the general GKN-EM theorem ⋮ Orthogonal polynomials and higher order singular Sturm-Liouville systems ⋮ Spectral analysis of the sixth-order Krall differential expression ⋮ Left-definite theory with applications to orthogonal polynomials ⋮ Self-adjoint operators generated from non-Lagrangian symmetric differential equations having orthogonal polynomial eigenfunctions
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