Abstract
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.
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Communicated by Edward B. Saff.
Research supported by NSF grant DMS1362208.
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Lubinsky, D.S. On Uniform Convergence of Diagonal Multipoint Padé Approximants for Entire Functions. Constr Approx 49, 149–174 (2019). https://doi.org/10.1007/s00365-017-9391-5
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DOI: https://doi.org/10.1007/s00365-017-9391-5