English

Direct and Inverse Results for Multipoint Hermite-Pade Approximants

Complex Variables 2018-10-17 v1

Abstract

Given a system of functions f = (f1, . . . , fd) analytic on a neighborhood of some compact subset E of the complex plane, we give necessary and sufficient conditions for the convergence with geometric rate of the common denominators of multipoint Hermite-Pade approximants. The exact rate of convergence of these denominators and of the approximants themselves is given in terms of the analytic properties of the system of functions. These results allow to detect the location of the poles of the system of functions which are in some sense closest to E.

Keywords

Cite

@article{arxiv.1810.07061,
  title  = {Direct and Inverse Results for Multipoint Hermite-Pade Approximants},
  author = {N. Bosuwan and G. Lopez Lagomasino and Y. Zaldivar Gerpe},
  journal= {arXiv preprint arXiv:1810.07061},
  year   = {2018}
}

Comments

18 pages. arXiv admin note: text overlap with arXiv:1606.07920, arXiv:1801.03004, arXiv:1203.4947