Inverse Theorem on Row Sequences of Linear Pade-orthogonal Approximation

We give necessary and sufficient conditions for the convergence with geometric rate of the denominators of linear Pade-orthogonal approximants corresponding to a measure supported on a general compact set in the complex plane. Thereby, we obtain an analog of Gonchar's theorem on row sequences of Pade approximants.The research of N. Bosuwan is supported by Mahidol University. The research of G. López Lagomasino is supported by Ministerio de Economía y Competitividad under Grant MTM2012-36732-C03-01