Calle Ysern, Bernardo de laLópez Lagomasino, Guillermo2010-01-112010-01-112001-04Journal of Approximation Theory, 2001, vol. 109, n. 2, p. 257-2780021-9045https://hdl.handle.net/10016/633722 pages, no figures.-- MSC2000 code: 41A21.MR#: MR1820896 (2002a:41014)Zbl#: Zbl 0982.41008Let μ be a finite positive Borel measure whose support is a compact subset K of the real line and let I be the convex hull of K. Let r denote a rational function with real coefficients whose poles lie in $\bbfC\setminus I\$ and $r(\infty)=0$. We consider multipoint rational interpolants of the function $$ f(z)=\int {d\mu(x)\over z-x}+r(z) $$, where some poles are fixed and others are left free. We show that if the interpolation points and the fixed poles are chosen conveniently then the sequence of multipoint rational approximants converges geometrically to f in the chordal metric on compact subsets of $\bbfC\setminus I\$.application/pdfeng© ElsevierPadé-type approximationRational approximationMulti-point approximationInterpolationGeometric convergenceChordal metricCapacityPre-assigned polesresearch articleMatemáticas10.1006/jath.2000.3537open access