Direct and inverse results on row sequences of simultaneous rational approximants

  1. Cacoq, Junot
Supervised by:
  1. Bernardo de la Calle Ysern Director
  2. Guillermo Tomás López Lagomasino Director

Defence university: Universidad Carlos III de Madrid

Fecha de defensa: 15 October 2012

Committee:
  1. Francisco Marcellán Español Chair
  2. Ramón Angel Orive Rodríguez Secretary
  3. Jeffrey S. Geronimo Committee member
  4. Manuel Bello Hernández Committee member
  5. Dolores Barrios Rolanía Committee member

Type: Thesis

Abstract

In this Tesis we investigate the approximation of vector functions by vector rational function that generalizes Padé approximants. We consider two types of approximants: the simultaneous Hermite-Padé approximants, which are constructed by mean of interpolation criterion and Fourier-Padé approximants based on Fourier series expansions in terms of a system of orthogonal polynomials. The results obtained in terms of generalize to the vector case results well known for the scalar case due to R. of Montessus of Ballore, A.A. Gonchar, S.P. Suetin, P.R. Graves-Morris, and E. B. Saff. ------------------------------------------------------------------------------------------------------------------------------------------------------------------------------------