The multidimensional generalization of g-fractions and their application

In this paper we consider the multidimensional g-fraction which is generalization of the continued g-fraction. We investigate the convergence of such fraction in the domain⋃α∈(−π/2,π/2) z=(z1,z2,…,zN)∈CN: ∑k=1N (|zk|−Re(zke−2iα))<2 cos2 α.We construct the algorithm for expansion of the formal N-multiple power series to the corresponding multidimensional g-fraction and also established the conditions of existence of such algorithm.