Distribution of interpolation points of maximally convergent multipoint Padé approximants

The paper investigates the distribution of interpolation points of m1m1-maximally convergent multipoint Padé approximants with numerator degree ≤n≤n and denominator degree ≤mn≤mn for meromorphic functions ff on a compact set E⊂CE⊂C, where mn=o(n/logn)mn=o(n/logn) as n→∞n→∞. It is shown that the normalized counting measures (resp. their associated balayage measures onto the boundary of EE) converge for a subsequence in the weak* sense to the equilibrium measure μEμE of EE if the multipoint Padé approximants for one single function ff converge exactly in m1m1-measure on the maximal Green domain of meromorphy Eρ(f)Eρ(f).