Laguerre-Sobolev orthogonal polynomials

DOI10.1016/0377-0427(95)00234-0zbMath0855.33015OpenAlexW2005988701MaRDI QIDQ1919955

Miguel A. Piñar, Teresa E. Pérez, Francisco Marcellán

Publication date: 28 July 1996

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

Full work available at URL: https://doi.org/10.1016/0377-0427(95)00234-0

zbMATH Keywords

Laguerre polynomialsChristoffel-Darboux-type relationdifference-differential relationRodrigues-type relation

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Other functions coming from differential, difference and integral equations (33E30)

Related Items (24)

Zeros of Sobolev orthogonal polynomials following from coherent pairs ⋮ Hermite-Sobolev and closely connected orthogonal polynomials ⋮ Logarithmic asymptotics of contracted Sobolev extremal polynomials on the real line ⋮ An asymptotic result for Laguerre-Sobolev orthogonal polynomials ⋮ Coherent pairs of measures and Markov-Bernstein inequalities ⋮ Connection coefficients for Laguerre--Sobolev orthogonal polynomials. ⋮ On generating Sobolev orthogonal polynomials ⋮ Some remarks on a paper by L. Carlitz ⋮ On asymptotic properties of Freud--Sobolev orthogonal polynomials. ⋮ From Standard Orthogonal Polynomials to Sobolev Orthogonal Polynomials: The Role of Semiclassical Linear Functionals ⋮ On Sobolev orthogonal polynomials ⋮ A Cohen-Type Inequality for Fourier Expansions with Respect to Non-Discrete Laguerre–Sobolev Inner Product ⋮ On Sobolev orthogonal polynomials with coherent pairs: The Laguerre case, type 1 ⋮ Asymptotics of Sobolev orthogonal polynomials for coherent pairs of Laguerre type ⋮ Inner products involving \(q\)-differences: The little \(q\)-Laguerre-Sobolev polynomials ⋮ Inner products involving differences: the meixner—sobolev polynomials ⋮ Connection problems for polynomial solutions of nonhomogeneous differential and difference equations ⋮ Some properties of the Sobolev-Laguerre polynomials ⋮ On the positivity of some bilinear functionals in Sobolev spaces ⋮ Sobolev orthogonal polynomials on product domains ⋮ Zeros of Sobolev orthogonal polynomials of Hermite type ⋮ Best polynomial approximation in Sobolev-Laguerre and Sobolev-Legendre spaces. ⋮ Zeros of Sobolev orthogonal polynomials of Gegenbauer type ⋮ A generating function for Laguerre-Sobolev orthogonal polynomials.

Cites Work

• On polynomials orthogonal with respect to certain Sobolev inner products
• An introduction to the numerical analysis of spectral methods. (Transl. of report CEA-N-2278, dated 1981, of the French Atomic Energy Commission, titled `Analyse numérique des méthodes spectrales')
• Coherent pairs and zeros of Sobolev-type orthogonal polynomials
• Orthogonal polynomials on Sobolev spaces: Old and new directions
• Error estimates for spectral approximation of linear advection equations over an hypercube
• Eine Erweiterung des Orthogonalitätsbegriffes bei Polynomen und deren Anwendung auf die beste Approximation.
• Zero Distribution and Behavior of Orthogonal Polynomials in the Sobolev Space $W^{1,2} [ - 1,1$]
• Zu den Orthogonalpolynomen von Althammer.
• Polynomial Least Square Approximations
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