Title: Asymptotics of Hermite-Padé rational approximants for two analytic functions with separated pairs of branch points (case of genus 0)
Authors: Aptekarev, Alexander
Kuijlaars, Arno
Van Assche, Walter # ×
Issue Date: 2008
Publisher: Oxford University Press
Series Title: International Mathematics Research Papers pages:rpm007
Abstract: We investigate the asymptotic behavior for type II Hermite–Padé approximation to two functions, where each function has two branch points and the pairs of branch points are
separated. We give a classification of the cases such that the limiting counting measures for the poles of the Hermite–Padé approximants are described by an algebraic function h of order 3 and genus 0. This situation gives rise to a vector-potential equilibrium problem for measures λ, μ1, and μ2, and the poles of the common denominator are asymptotically
distributed like λ/2. We also work out the strong asymptotics for the corresponding Hermite–Padé approximants by using a 3×3 Riemann–Hilbert problem that characterizes
this Hermite–Padé approximation problem.
ISSN: 1687-3017
Publication status: published
KU Leuven publication type: IT
Appears in Collections:Analysis Section
× corresponding author
# (joint) last author

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