Mathematics – Classical Analysis and ODEs
Scientific paper
2007-08-07
International Mathematics Research Papers 2008, rpm007 (128 pp.)
Mathematics
Classical Analysis and ODEs
102 pages, 31 figures
Scientific paper
10.1093/imrp/rpm007
We investigate the asymptotic behavior for type II Hermite-Pade 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-Pade approximants are described by an algebraic function of order 3 and genus 0. This situation gives rise to a vector-potential equilibrium problem for three measures and the poles of the common denominator are asymptotically distributed like one of these measures. We also work out the strong asymptotics for the corresponding Hermite-Pade approximants by using a 3x3 Riemann-Hilbert problem that characterizes this Hermite-Pade approximation problem.
Aptekarev Alexander I.
Assche Walter Van
Kuijlaars Arno B. J.
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