Bosuwan, NattapongLópez Lagomasino, Guillermo2023-09-112023-09-112019-04Bosuwan, N., & López Lagomasino, G. (2019). Direct and inverse results on row sequences of simultaneous Padé–Faber approximants. Mediterranean Journal of Mathematics, 16(2), 36.1660-5446https://hdl.handle.net/10016/38288Given a vector function F=(F1,...,Fd), analytic on a neighborhood of some compact subset E of the complex plane with simply connected complement, we define a sequence of vector rational functions with common denominator in terms of the expansions of the components Fk,k=1,...,d, with respect to the sequence of Faber polynomials associated with E. Such sequences of vector rational functions are analogous to row sequences of type II Hermite-Pade approximation. We give necessary and sufficient conditions for the convergence with geometric rate of the common denominators of the sequence of vector rational functions so constructed. The exact rate of convergence of these denominators is provided and the rate of convergence of the approximants is estimated. It is shown that the common denominators of the approximants detect the poles of the system of functions closest to E and their order.21eng© Springer Nature Switzerland AG 2019Montessus de Ballore's theoremFaber polynomialsSimultaneous approximationHermite-Pade approximationRate of convergenceInverse resultsConvergenceresearch articleMatemáticashttps://doi.org/10.1007/s00009-019-1307-0open access12, 3621Mediterranean Journal of Mathematics16AR/0000023342