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Multipoint rational approximants with preassigned poles

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URI: https://hdl.handle.net/10016/6352
ISSN: 0022-247X
DOI: 10.1006/jmaa.2000.7299
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multipoint_lagomasino_jmaa_2001_ps.pdf (204.75 KB)
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2001-04
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Elsevier
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Abstract
Let $\mu$ be a finite positive Borel measure whose support $S(\mu)$ is a compact regular set contained in $\Bbb R$. For a function of Markov type $\hat\mu(z)=\int_{S(\mu)}d\mu(x)/(z-x)$, $z\in\Bbb C\sbs S(\mu)$, we consider multipoint Padé-type approximants (MPTAs), where some poles are preassigned and interpolation is carried out along a table of points contained in $\overline{\Bbb C}\sbs {\rm Co}(S(\mu))$ which is symmetrical with respect to the real line. The main purpose of this paper is the study of the `exact rate of convergence' of the MPTAs to the function $\hat\mu$.
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20 pages, no figures.-- MSC1991 codes: 41A21, 42C05, 30E10.
MR#: MR1820073 (2002i:41021)
Zbl#: Zbl 1160.41305
Keywords
Orthogonal polynomials, Logarithmic potential, Padé-type approximants, Rate of convergence
Bibliographic citation
Journal of Mathematical Analysis and Applications, 2001, vol. 256, n. 1, p. 142-161
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