RT Journal Article
T1 Asymptotic behaviour of Sobolev-type orthogonal polynomials on a rectifiable Jordan arc
A1 Branquinho, A.
A1 Moreno, Ana F.
A1 Marcellán Español, Francisco José
AB 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 $E$.
PB Springer
SN 0176-4276 (Print)
SN 1432-0940 (Online)
YR 2002
FD 2002-10
LK https://hdl.handle.net/10016/6065
UL https://hdl.handle.net/10016/6065
LA eng
NO 22 pages, no figures.-- MSC2000 codes: Primary 42C05.
NO MR#: MR1890494 (2002m:42023)
NO Zbl#: Zbl 0991.42018
NO The work of the first author was supported by the Portuguese Ministry of Science and Technology, Fundação para a Ciência e Tecnología of Portugalunder grant FMRH-BSAB-109-99 and by the Centro de Matemática da Universidade de Coimbra. The second author would also like to thank the Unidade de Investigação (Matemática e Aplicações) of the University of Aveiro for their support. The work of the second and third authors was supported by the Dirección General de Enseñanza Superior(DGES) of Spain under grant PB 96-0120-C03-01.
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RD 18 may. 2024