Cita:
Journal of Mathematical Analysis and Applications, 2001, vol. 256, n. 1, p. 142-161
ISSN:
0022-247X
DOI:
10.1006/jmaa.2000.7299
Patrocinador:
Research by first author (F.C.) partially carried out at the Mathematics Department of Umeå University under Guest Scholarship from the Swedish Institute. Research by second author (G.L.L.) partially supported by Dirección General de Enseñanza Superior under grant PB 96-0120-CO3-01 and by INTAS under grant 93-0219 EXT.
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 (MLet $\mu$ 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 $\hat\mu$.[+][-]
Nota:
20 pages, no figures.-- MSC1991 codes: 41A21, 42C05, 30E10.
