Strong asymptotics for Gegenbauer-Sobolev orthogonal polynomials

Andrei Martínez-Finkelshtein; Juan J. Moreno-Balcázar; Héctor Pijeira-Cabrera

doi:10.1016/S0377-0427(97)00059-9

Strong asymptotics for Gegenbauer-Sobolev orthogonal polynomials

Andrei Martínez-Finkelshtein, Juan J. Moreno-Balcázar, Héctor Pijeira-Cabrera

Research output: Contribution to journal › Article › peer-review

12 Scopus citations

Abstract

We study the asymptotic behaviour of the monic orthogonal polynomials with respect to the Gegenbauer-Sobolev inner product (f,g)s = 〈f,g〉 + λ〈f′,g′〉 where 〈f,g〉 = ∫¹_-1 f(x)g(x)(1 - x²)^α-1/2 dx with α>-1/2 and λ>0. The asymptotics of the zeros and norms of these polynomials are also established.

Original language	English
Pages (from-to)	211-216
Number of pages	6
Journal	Journal of Computational and Applied Mathematics
Volume	81
Issue number	2
DOIs	https://doi.org/10.1016/S0377-0427(97)00059-9
State	Published - 8 Jul 1997
Externally published	Yes

Keywords

Asymptotics
Sobolev orthogonal polynomials

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

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10.1016/S0377-0427(97)00059-9

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title = "Strong asymptotics for Gegenbauer-Sobolev orthogonal polynomials",

abstract = "We study the asymptotic behaviour of the monic orthogonal polynomials with respect to the Gegenbauer-Sobolev inner product (f,g)s = 〈f,g〉 + λ〈f′,g′〉 where 〈f,g〉 = ∫1-1 f(x)g(x)(1 - x2)α-1/2 dx with α>-1/2 and λ>0. The asymptotics of the zeros and norms of these polynomials are also established.",

keywords = "Asymptotics, Sobolev orthogonal polynomials",

author = "Andrei Mart{\'i}nez-Finkelshtein and Moreno-Balc{\'a}zar, \{Juan J.\} and H{\'e}ctor Pijeira-Cabrera",

year = "1997",

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TY - JOUR

T1 - Strong asymptotics for Gegenbauer-Sobolev orthogonal polynomials

AU - Martínez-Finkelshtein, Andrei

AU - Moreno-Balcázar, Juan J.

AU - Pijeira-Cabrera, Héctor

PY - 1997/7/8

Y1 - 1997/7/8

N2 - We study the asymptotic behaviour of the monic orthogonal polynomials with respect to the Gegenbauer-Sobolev inner product (f,g)s = 〈f,g〉 + λ〈f′,g′〉 where 〈f,g〉 = ∫1-1 f(x)g(x)(1 - x2)α-1/2 dx with α>-1/2 and λ>0. The asymptotics of the zeros and norms of these polynomials are also established.

AB - We study the asymptotic behaviour of the monic orthogonal polynomials with respect to the Gegenbauer-Sobolev inner product (f,g)s = 〈f,g〉 + λ〈f′,g′〉 where 〈f,g〉 = ∫1-1 f(x)g(x)(1 - x2)α-1/2 dx with α>-1/2 and λ>0. The asymptotics of the zeros and norms of these polynomials are also established.

KW - Asymptotics

KW - Sobolev orthogonal polynomials

UR - https://www.scopus.com/pages/publications/0031559379

U2 - 10.1016/S0377-0427(97)00059-9

DO - 10.1016/S0377-0427(97)00059-9

M3 - Article

AN - SCOPUS:0031559379

SN - 0377-0427

VL - 81

SP - 211

EP - 216

JO - Journal of Computational and Applied Mathematics

JF - Journal of Computational and Applied Mathematics

IS - 2

ER -

Strong asymptotics for Gegenbauer-Sobolev orthogonal polynomials

Abstract

Keywords

ASJC Scopus subject areas

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