Classical and Sobolev orthogonality of the nonclassical Jacobi polynomials with parameters \(\alpha =\beta =-1\)

DOI10.1007/S10231-012-0284-8zbMath1296.33018arXiv1205.5085OpenAlexW1979778992MaRDI QIDQ2014999

Lance L. Littlejohn, Andrea Bruder

Publication date: 18 June 2014

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1205.5085

zbMATH Keywords

Sobolev spaceJacobi polynomialsself-adjoint operatororthogonalityleft-definite operator theory

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Weyl theory and its generalizations for ordinary differential equations (34B20) Linear symmetric and selfadjoint operators (unbounded) (47B25) Positive linear operators and order-bounded operators (47B65) Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) (34B30)

Related Items (1)

Singular left-definite Hamiltonian systems in the Sobolev space

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• The Sobolev orthogonality and spectral analysis of the Laguerre polynomials \(\{L_{n}^{-k}\}\) for positive integers \(k\)
• Legendre-Stirling permutations
• Combinatorial interpretations of the Jacobi-Stirling numbers
• Sobolev orthogonal polynomials and second-order differential equations
• Sobolev orthogonality for the Gegenbauer polynomials \(\{ C_n^{-N+1/2}\}_{n\geq 0}\)
• An integral operator inequality with applications
• Sobolev orthogonal polynomials: The discrete-continuous case
• Orthogonality of the Jacobi polynomials with negative integer parameters
• A general left-definite theory for certain self-adjoint operators with applications to differential equations
• The Jacobi-Stirling numbers
• Nonclassical Jacobi polynomials and Sobolev orthogonality
• The Legendre-Stirling numbers
• Jacobi-Stirling numbers, Jacobi polynomials, and the left-definite analysis of the classical Jacobi differential expression
• A combinatorial interpretation of the Legendre-Stirling numbers
• Osservazioni sopra una classe di disuguaglianze
• Hardy's inequality with weights
• Sobolev Spaces

This page was built for publication: Classical and Sobolev orthogonality of the nonclassical Jacobi polynomials with parameters \(\alpha =\beta =-1\)