THE CONVERGENCE OF PADE-TYPE APPROXIMANTS TO HOLOMORPHIC-FUNCTIONS OF SEVERAL COMPLEX-VARIABLES

Our main purpose is to discuss the convergence of Padé-type approximants to a function which is holomorphic in an open subset Ω of Cn (n>1). If n=1, a general method due to Eiermann gives the basic result [6]. This paper contains: (a) the study of some typical cases: Ω is an open polydisk centered at 0 and Ω=Cn; (b) an answer to the question whether the approximation of a holomorphic function by a sequence of Padé-type approximants is possible; (c) four examples of Padé-type approximants converging to holomorphic functions, if n=2. © 1990.