A ug 2 00 7 Asymptotics of Hermite - Padé rational approximants for two analytic functions with separated pairs of branch points ( case of genus 0
نویسندگان
چکیده
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.
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