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E. Berriochoa, A. Cachafeiro, J. García-Amor (2005)
Asymptotic properties of Chebyshev-Sobolev orthogonal polynomialsJournal of Computational and Applied Mathematics, 178
Berriochoa, Cachafeiro (2003)
On the Strong Asymptotics for Sobolev Orthogonal Polynomials on the CircleConstructive Approximation, 19
P. Túrán (1975)
On orthogonal polynomialsAnalysis Mathematica, 1
W. Gautschi, A. Kuijlaars (1997)
Zeros and Critical Points of Sobolev Orthogonal PolynomialsJournal of Approximation Theory, 91
J. Walsh (1935)
Interpolation and Approximation by Rational Functions in the Complex Domain
F. Marcellán, W. Assche (1993)
Relative asymptotics for orthogonal polynomialsJ. Approx. Theory, 72
F. Marcellán, W. Vanassche (1993)
Relative Asymptotics for Orthogonal Polynomials with a Sobolev Inner ProductJournal of Approximation Theory, 72
G. L'opez, F. Marcellán, W. Assche (1994)
Relative asymptotics for polynomials orthogonal with respect to a discrete Sobolev inner productConstructive Approximation, 11
A. Martínez-Finkelshtein (2000)
Bernstein—Szegő's Theorem for Sobolev Orthogonal PolynomialsConstructive Approximation, 16
A. Martínez-Finkelshtein (1998)
Asymptotic properties of Sobolev orthogonal polynomialsJournal of Computational and Applied Mathematics, 99
A. Aptekarev, E. Berriochoa, A. Cachafeiro (1999)
Strong asymptotics for the continuous Sobolev Orthogonal polynomials on the unit circleJournal of Approximation Theory, 100
F. Marcellán, M. Alfaro, M. Rezola (1993)
Orthogonal polynomials on Sobolev spaces: old and new directionsJournal of Computational and Applied Mathematics, 48
In this paper we show the connection between Sobolev orthogonal Laurent polynomials on the unit circle and Sobolev orthogonal polynomials on a bounded interval of the real line. As a consequence we deduce the strong outer asymptotics for Sobolev orthogonal polynomials with respect to the inner product $$\langle f(x),g(x)\rangle_{s_{\mu}}=\int_{-1}^{1}f(x)g(x)\,\mathrm{d}\mu _{0}(x)+\int_{-1}^{1}f'(x)g'(x)\,\mathrm{d}\mu _{1}(x),$$ assuming that μ1 belongs to the Szegő class as well as (1−x 2)−1∈L 1(μ1).
Acta Applicandae Mathematicae – Springer Journals
Published: Dec 1, 2004
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