On Montessus de Ballore’s theorem for simultaneous Padé-Faber approximants

Abstract

We consider row sequences of vector valued Padé-Faber approximants (simultaneous Padé-Faber approximants) and prove a Montessus de Ballore type theorem. Moreover, we provide a comparison between this new Montessus de Ballore type theorem and the Montessus de Ballore type theorem in Bosuwan (Math. Notes, 2018, 103).

Keywords

• Montessus de Ballore’s theorem
• Padé-Faber approximants
• simultaneous Padé approximants
• Hermite-Padé approximants
• Primary 30E10
• Secondary 41A21