Convergence versus correspondence for sequences of rational functions

• Published in: Indagationes mathematicae Vol. 12; no. 2; pp. 213 - 219
• Main Authors: Lorentzen, L., Lubinsky, D.S.
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 18.06.2001

Let f be meromorphic in the plane and analytic at 0. Then its diagonal sequence {[ n/n]} ∞ n = 1 of Padé approximants need not converge pointwise. We ask whether by reducing the order of contact (or correspondence) of [ n/n] with f at 0, namely 2 n + 1, we can ensure locally uniform convergence. In...