Asymptotics of Sobolev Orthogonal Polynomials for Coherent Pairs of Measures

Andrei Martínez-Finkelshtein; Juan J. Moreno-Balcázar; Teresa E. Pérez; Miguel A. Piñar

doi:10.1006/jath.1997.3123

Asymptotics of Sobolev Orthogonal Polynomials for Coherent Pairs of Measures

Andrei Martínez-Finkelshtein, Juan J. Moreno-Balcázar, Teresa E. Pérez, Miguel A. Piñar

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

33 Scopus citations

Abstract

Strong asymptotics for the sequence of monic polynomialsQ_n(z), orthogonal with respect to the inner product(f, g)_S=∫f(x)g(x)dμ₁(x)+λ∫ f′(x)g′(x)dμ₂(x),λ>0,withzoutside of the support of the measureμ₂, is established under the additional assumption thatμ₁andμ₂form a so-called coherent pair with compact support. Moreover, the asymptotic behaviour of the (square of) the norm (Q_n, Q_n)_Sand of the zeros ofQ_nis obtained.

Original language	English
Pages (from-to)	280-293
Number of pages	14
Journal	Journal of Approximation Theory
Volume	92
Issue number	2
DOIs	https://doi.org/10.1006/jath.1997.3123
State	Published - 1 Feb 1998
Externally published	Yes

Keywords

Sobolev orthogonal polynomials; asymptotics; coherent pairs of measures

ASJC Scopus subject areas

Analysis
Numerical Analysis
General Mathematics
Applied Mathematics

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10.1006/jath.1997.3123

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abstract = "Strong asymptotics for the sequence of monic polynomialsQn(z), orthogonal with respect to the inner product(f, g)S=∫f(x)g(x)dμ1(x)+λ∫ f′(x)g′(x)dμ2(x),λ>0,withzoutside of the support of the measureμ2, is established under the additional assumption thatμ1andμ2form a so-called coherent pair with compact support. Moreover, the asymptotic behaviour of the (square of) the norm (Qn, Qn)Sand of the zeros ofQnis obtained.",

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AU - Moreno-Balcázar, Juan J.

AU - Pérez, Teresa E.

AU - Piñar, Miguel A.

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AB - Strong asymptotics for the sequence of monic polynomialsQn(z), orthogonal with respect to the inner product(f, g)S=∫f(x)g(x)dμ1(x)+λ∫ f′(x)g′(x)dμ2(x),λ>0,withzoutside of the support of the measureμ2, is established under the additional assumption thatμ1andμ2form a so-called coherent pair with compact support. Moreover, the asymptotic behaviour of the (square of) the norm (Qn, Qn)Sand of the zeros ofQnis obtained.

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ER -

Asymptotics of Sobolev Orthogonal Polynomials for Coherent Pairs of Measures

Abstract

Keywords

ASJC Scopus subject areas

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