Publication: Direct and inverse results for multipoint Hermite-Padé approximants
Loading...
Identifiers
Publication date
2019-06
Defense date
Advisors
Tutors
Journal Title
Journal ISSN
Volume Title
Publisher
Springer Nature
Impact
Export
Abstract
Given a system of functions f = ( f1,..., fd ) analytic on a neighborhood of some compact subset E of the complex plane with simply connected complement in the extended complex plane, we give necessary and sufficient conditions for the convergence with geometric rate of the common denominators of row sequences of multipoint Hermite–Padé approximants under a general extremal condition on the table of interpolation points. The exact rate of convergence of these denominators is provided and the rate of convergence of the simultaneous approximants is estimated. These results allow us to detect the location of the poles of the system of functions which are in some sense closest to E.
Description
Special Issue: Complex Analysis, Potential Theory and Applications
Keywords
Hermite-Padé approximation, Inverse type results, Montessus de Ballore theorem, Multipoint Padé approximation
Bibliographic citation
Bosuwan, N., López Lagomasino, G., & Zaldivar Gerpe, Y. (2019). Direct and inverse results for multipoint Hermite–Padé approximants. Analysis and Mathematical Physics, 9(2), 761–779.