Convergence in Hausdorff Content of Pade-Faber Approximants and Its Applications

Nattapong Bosuwan, Waraporn Chonlapap

Abstract

A convergence in Hausdorff content of Pade-Faber approximants (recently introduced) on some certain sequences is proved. As applications of this result, we give an alternate proof of a Montessus de Ballore type theorem for these  Pade-Faber approximants and a proof of a convergence of Pade-Faber approximants in the maximal canonical domain in which the approximated function can be continued to a meromorphic function.