The Sobolev orthogonality and spectral analysis of the Laguerre polynomials \(\{L_{n}^{-k}\}\) for positive integers \(k\)

DOI10.1016/j.cam.2004.01.017zbMath1063.33009OpenAlexW2033553047MaRDI QIDQ596242

Lance L. Littlejohn, W. Norrie Everitt, Richard Wellman

Publication date: 10 August 2004

Published in: Journal of Computational and Applied Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.cam.2004.01.017

zbMATH Keywords

Sobolev spacesorthogonal polynomialsLaguerre polynomialsself-adjoint operatorsleft-definite theory

Mathematics Subject Classification ID

Sturm-Liouville theory (34B24) Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Orthogonal functions and polynomials, general theory of nontrigonometric harmonic analysis (42C05) Boundary value problems on infinite intervals for ordinary differential equations (34B40)

Related Items (15)

A general left-definite theory for certain self-adjoint operators with applications to differential equations ⋮ A conjecture on exceptional orthogonal polynomials ⋮ Nonclassical Jacobi polynomials and Sobolev orthogonality ⋮ On self-adjoint boundary conditions for singular Sturm-Liouville operators bounded from below ⋮ Some remarks on a paper by L. Carlitz ⋮ A spectral study of the second-order exceptional \(X_1\)-Jacobi differential expression and a related non-classical Jacobi differential expression ⋮ Some progress in spectral methods ⋮ Characterizations of distributional weights for weak orthogonal polynomials satisfying a second-order differential equation ⋮ Sobolev orthogonal polynomials of several variables on product domains ⋮ Jacobi and Laguerre quasi-orthogonal approximations and related interpolations ⋮ An extension of Bochner's problem: exceptional invariant subspaces ⋮ Classical and Sobolev orthogonality of the nonclassical Jacobi polynomials with parameters \(\alpha =\beta =-1\) ⋮ Orthogonal polynomial solutions of linear ordinary differential equations ⋮ An extended class of orthogonal polynomials defined by a Sturm-Liouville problem ⋮ Left-definite theory with applications to orthogonal polynomials

Cites Work

• Laguerre polynomial expansions in indefinite inner product spaces
• Sobolev orthogonal polynomials and second-order differential equations
• An integral operator inequality with applications
• A general left-definite theory for certain self-adjoint operators with applications to differential equations
• Osservazioni sopra una classe di disuguaglianze
• Hardy's inequality with weights
• Generating Functions for Bessel and Related Polynomials
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