Publication: Asymptotic behaviour of Sobolev-type orthogonal polynomials on a rectifiable Jordan arc
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ISSN: 0176-4276 (Print)
ISSN: 1432-0940 (Online)
Publication date
2002-10
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Tutors
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Springer
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Abstract
Our object of study is the asymptotic behavior of the sequence of polynomials orthogonal with respect to the discrete Sobolev inner product $$\langle f, g \rangle = \int_{E} f(\xi) \overline{g(\xi)} \rho (\xi) \xi \xi f(Z) A g(Z)^H,$$ where $E$ is a rectifiable Jordan curve or arc in the complex plane $$f(Z) = (f(z_1), \ldots, f^{(l_1)}(z_1) , \ldots , f(z_m) , \ldots ,f^{(l_m)}(z_m)),$$ $A$ is an $M \times M$ Hermitian matrix, $M=l_{1} + \cdots + l_{m} + m$, $ denotes the arc length measure, $\rho$ is a nonnegative function on $E$ , and $z_{i} \in \Omega$, $i=1,2,\ldots,m$, where $\Omega$ is the exterior region to $E$.
Description
22 pages, no figures.-- MSC2000 codes: Primary 42C05.
MR#: MR1890494 (2002m:42023)
Zbl#: Zbl 0991.42018
MR#: MR1890494 (2002m:42023)
Zbl#: Zbl 0991.42018
Keywords
Orthogonal polynomials, Sobolev inner products, Asymptotics, Jordan curves
Bibliographic citation
Constructive Approximation, 2002, vol. 18, n. 2, p. 161-182