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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 analogue of Gonchars theorem on row sequences of Pade approximants.
Starting from the orthogonal polynomial expansion of a function $F$ corresponding to a finite positive Borel measure with infinite compact support, we study the asymptotic behavior of certain associated rational functions (Pad{e}-orthogonal approxima
Given a vector function ${bf F}=(F_1,ldots,F_d),$ analytic on a neighborhood of some compact subset $E$ of the complex plane with simply connected complement, we define a sequence of vector rational functions with common denominator in terms of the e
We consider row sequences of vector valued Pad{e}-Faber approximants (simultaneous Pad{e}-Faber approximants) and prove a Montessus de Ballore type theorem.
Given a system of functions f = (f1, . . . , fd) analytic on a neighborhood of some compact subset E of the complex plane, we give necessary and sufficient conditions for the convergence with geometric rate of the common denominators of multipoint He
Let $f$ be a power series with positive radius of convergence. In the present paper, we study the phenomenon of overconvergence of sequences of classical Pade approximants pi{n,m_n} associated with f, where m(n)<=m(n+1)<=m(n) and m(n) = o(n/log n), r