Divergence of vector-valued rational interpolations to meromorphic functions (Q1178586)

The authors consider vector-valued rational interpolants whose confluent form is also known as simultaneous Padé approximants. In a previous paper of the same authors [Rational approximation and interpolation, Proc. Conf., Tampa/Fla. 1983, Lect. Notes Math. 1105, 227-242 (1984; Zbl 0554.41025)], they prove a Montessus de Ballore type theorem for such approximants. For classical Padé approximants, the divergence outside a certain disk was established by H. Stahl in 1976. The same result was independently obtained by \textit{V. V. Vavilov} [Mat. Sb., Nov. Ser. 101(143), 44-56 (1976; Zbl 0341.41014)]. Here, an analogous result is proved for vector-valued Padé approximants. Finally, they state the corresponding theorem for the more general case of vector-valued rational interpolants.