Publication: Direct and inverse results on row sequences of simultaneous Pade-Faber approximants
Loading...
Identifiers
Publication date
2019-04
Defense date
Advisors
Tutors
Journal Title
Journal ISSN
Volume Title
Publisher
Springer Nature
Impact
Export
Abstract
Given 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.
Description
Keywords
Montessus de Ballore's theorem, Faber polynomials, Simultaneous approximation, Hermite-Pade approximation, Rate of convergence, Inverse results, Convergence
Bibliographic citation
Bosuwan, N., & López Lagomasino, G. (2019). Direct and inverse results on row sequences of simultaneous Padé–Faber approximants. Mediterranean Journal of Mathematics, 16(2), 36.