Constructive Approximation

, Volume 49, Issue 1, pp 149–174 | Cite as

On Uniform Convergence of Diagonal Multipoint Padé Approximants for Entire Functions

  • D. S. LubinskyEmail author


We prove that for most entire functions f in the sense of category, a strong form of the Baker–Gammel–Wills conjecture holds. More precisely, there is an infinite sequence \({\mathcal {S}}\) of positive integers n, such that given any \(r>0\), and multipoint Padé approximants \(R_{n}\) to f with interpolation points in \(\left\{ z:\left| z\right| \le r\right\} \), \(\left\{ R_{n}\right\} _{n\in S}\) converges locally uniformly to f in the plane. The sequence \({\mathcal {S}}\) does not depend on r, or on the interpolation points. For entire functions with smooth rapidly decreasing coefficients, full diagonal sequences of multipoint Padé approximants converge.


Padé approximation Multipoint Padé approximants Spurious poles 

Mathematics Subject Classification

41A21 41A20 30E10 


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© Springer Science+Business Media, LLC 2017

Authors and Affiliations

  1. 1.School of MathematicsGeorgia Institute of TechnologyAtlantaUSA

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