Analytic aspects of Sobolev orthogonal polynomials revisited

DOI10.1016/S0377-0427(00)00499-4zbMath0971.33004MaRDI QIDQ5929301

Andrei Martínez-Finkelshtein

Publication date: 14 June 2001

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

Mathematics Subject Classification ID

Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) (33C45) Research exposition (monographs, survey articles) pertaining to special functions (33-02)

Related Items (29)

Asymptotic properties of generalized Laguerre orthogonal polynomials. ⋮ The differential equation for Jacobi-Sobolev orthogonal polynomials with two linear perturbutions ⋮ Asymptotics and zeros of Sobolev orthogonal polynomials on unbounded supports ⋮ Some asymptotics for Sobolev orthogonal polynomials involving Gegenbauer weights ⋮ New steps on Sobolev orthogonality in two variables ⋮ Sobolev orthogonal polynomials on the unit circle and coherent pairs of measures of the second kind ⋮ Jacobi-Sobolev orthogonal polynomials: asymptotics and a Cohen type inequality ⋮ Weighted Sobolev orthogonal polynomials on the unit ball ⋮ Asymptotics for Jacobi-Sobolev orthogonal polynomials associated with non-coherent pairs of measures ⋮ The semiclassical Sobolev orthogonal polynomials: a general approach ⋮ Coherent pairs of measures of the second kind on the real line and Sobolev orthogonal polynomials. An application to a Jacobi case ⋮ Structure relations for orthogonal polynomials on the unit circle ⋮ On generating Sobolev orthogonal polynomials ⋮ Rational approximation and Sobolev-type orthogonality ⋮ Coherent pairs of moment functionals of the second kind and associated orthogonal polynomials and Sobolev orthogonal polynomials ⋮ On asymptotic properties of Freud--Sobolev orthogonal polynomials. ⋮ Sobolev orthogonal polynomials defined via gradient on the unit ball ⋮ On Sobolev orthogonal polynomials ⋮ Sobolev orthogonal polynomials of several variables on product domains ⋮ Analytic properties of some basic hypergeometric-Sobolev-type orthogonal polynomials ⋮ \(\Delta\)-Sobolev orthogonal polynomials of Meixner type: asymptotics and limit relation ⋮ The Laguerre-Sobolev-type orthogonal polynomials ⋮ A higher order Sobolev-type inner product for orthogonal polynomials in several variables ⋮ An extension of the coherent pair of measures of the second kind on the unit circle ⋮ New representations of the Laguerre-Sobolev and Jacobi-Sobolev orthogonal polynomials ⋮ Zeros and logarithmic asymptotics of Sobolev orthogonal polynomials for exponential weights ⋮ Sobolev–Gegenbauer-type orthogonality and a hydrodynamical interpretation ⋮ On some Sobolev spaces with matrix weights and classical type Sobolev orthogonal polynomials ⋮ Asymptotics on the support for Sobolev orthogonal polynomials on a bounded interval

Cites Work

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• The moment problem for a Sobolev inner product
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• Determination of all coherent pairs
• Zeros and critical points of Sobolev orthogonal polynomials
• An asymptotic result for Laguerre-Sobolev orthogonal polynomials
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• Inner products involving \(q\)-differences: The little \(q\)-Laguerre-Sobolev polynomials
• Nondiagonal Hermite-Sobolev orthogonal polynomials
• Asymptotic properties of balanced extremal Sobolev polynomials: Coherent case
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• On polynomials orthogonal with respect to an inner product involving differences
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• Ratio and Plancherel-Rotach asymptotics for Meixner-Sobolev orthogonal polynomials
• Orthogonal polynomials
• On Recurrence Relations for Sobolev Orthogonal Polynomials
• Sobolev orthogonal polynomials in the complex plane
• Strong and Plancherel-Rotach asymptotics of non-diagonal Laguerre-Sobolev orthogonal polynomials

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