Row convergence theorems for generalised inverse vector-valued Padé approximants

摘要

The approximants mentioned in the title are related to vector-valued continued fractions and the vector ϵ-algorithm devised by Wynn in 1963. Here we establish a unitary invariance property of these approximants and describe how the classical (1-dimensional) Padé approximants can be obtained as a special case. The main results of the paper consist of De Montessus—De Ballore type convergence theorems for row sequences (having fixed denominator degree) of vector-valued approximants to meromorphic vector functions.