Nonclassical Jacobi polynomials and Sobolev orthogonality

DOI10.1007/s00025-011-0102-4zbMath1259.33015OpenAlexW2160013479MaRDI QIDQ1930330

Andrea Bruder, Lance L. Littlejohn

Publication date: 10 January 2013

Published in: Results in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00025-011-0102-4

zbMATH Keywords

Sobolev orthogonalitynonclassical Jacobi polynomials

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) Higher logarithm functions (33B30)

Related Items (3)

Approximation by polynomials in Sobolev spaces associated with classical moment functionals ⋮ On Sobolev bilinear forms and polynomial solutions of second-order differential equations ⋮ Classical and Sobolev orthogonality of the nonclassical Jacobi polynomials with parameters \(\alpha =\beta =-1\)

Cites Work

• The Sobolev orthogonality and spectral analysis of the Laguerre polynomials \(\{L_{n}^{-k}\}\) for positive integers \(k\)
• 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
• Jacobi-Stirling numbers, Jacobi polynomials, and the left-definite analysis of the classical Jacobi differential expression
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