http://imrp.oxfordjournals.org International Mathematics Research Papers - RSS feed of current issue 1687-3009 2008 International Mathematics Research Papers 1687-3017 http://imrp.oxfordjournals.org/cgi/content/short/2008/rpm007/rpm007?rss=1 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 and genus 0. This situation gives rise to a vector-potential equilibrium problem for measures , µ₁, and µ₂, and the poles of the common denominator are asymptotically distributed like /2. We also work out the strong asymptotics for the corresponding Hermite–Padé approximants by using a 3 x 3 Riemann–Hilbert problem that characterizes this Hermite–Padé approximation problem.

]]> 2008-01-29 info:doi/10.1093/imrp/rpm007 Oxford University Press rpm007 2008 128 2008-01-29 rpm007 Research Articles