Asymptotic properties of Sobolev orthogonal polynomials

DOI10.1016/S0377-0427(98)00179-4zbMath0933.42013OpenAlexW2075234106MaRDI QIDQ1298589

Andrei Martínez-Finkelshtein

Publication date: 21 March 2000

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

Full work available at URL: https://doi.org/10.1016/s0377-0427(98)00179-4

zbMATH Keywords

Sobolev orthogonal polynomialsinner products involving derivativesstrong outer asymptotesweak asymptotes

Mathematics Subject Classification ID

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)

Related Items (21)

Asymptotic properties of generalized Laguerre orthogonal polynomials. ⋮ Asymptotics and zeros of Sobolev orthogonal polynomials on unbounded supports ⋮ The moment problem for a Sobolev inner product ⋮ Strong asymptotics for the continuous Sobolev orthogonal polynomials on the unit circle ⋮ Sobolev orthogonal polynomials on the unit circle and coherent pairs of measures of the second kind ⋮ 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 ⋮ Coherent pairs of moment functionals of the second kind and associated orthogonal polynomials and Sobolev orthogonal polynomials ⋮ On Sobolev orthogonal polynomials ⋮ An extremal problem for algebraic polynomials in the symmetric discrete Gegenbauer--Sobolev space ⋮ Sobolev orthogonal polynomials of several variables on product domains ⋮ Analytic aspects of Sobolev orthogonal polynomials revisited ⋮ Strong and Plancherel-Rotach asymptotics of non-diagonal Laguerre-Sobolev orthogonal polynomials ⋮ Orthogonal polynomial solutions of linear ordinary differential equations ⋮ Connections between interval and unit circle for Sobolev orthogonal polynomials. Strong asymptotics on the real line ⋮ A higher order Sobolev-type inner product for orthogonal polynomials in several variables ⋮ Strong asymptotics for Sobolev orthogonal polynomials ⋮ 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 ⋮ On some Sobolev spaces with matrix weights and classical type Sobolev orthogonal polynomials ⋮ On linearly related sequences of difference derivatives of discrete orthogonal polynomials

Cites Work

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• An asymptotic result for Laguerre-Sobolev orthogonal polynomials
• Asymptotics of Sobolev orthogonal polynomials for a Jacobi weight
• Asymptotics of Sobolev orthogonal polynomials for coherent pairs of measures
• Relative asymptotics for orthogonal polynomials with a Sobolev inner product
• Asymptotic properties of balanced extremal Sobolev polynomials: Coherent case
• Strong asymptotics for Sobolev orthogonal polynomials
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• On Recurrence Relations for Sobolev Orthogonal Polynomials
• Jentzsch-Szegö Type Theorems for the Zeros of Best Approximants
• Zu den Orthogonalpolynomen von Althammer.

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