Abstract
We prove that for entire functions f of finite order, there is a sequence of integers \(\mathcal {S}\) such that as \(n\rightarrow \infty \) through S,
uniformly for z in compact subsets of the plane. More generally this holds for sequences of Newton–Padé approximants and for functions whose errors of approximation by rational functions of type \(\left( n,n\right) \) decay sufficiently fast. This establishes George Baker’s patchwork conjecture for large classes of entire functions.
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Acknowledgements
The author thanks the referees for finding many misprints in the original version, as well as for suggestions that improved the presentation, and the reference [11].
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Communicated by Edward B. Saff.
In memory of George A. Baker. Jr., November 25, 1932- July 24, 2018.
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Research supported by NSF Grant DMS1800251.
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Lubinsky, D.S. On Baker’s Patchwork Conjecture for Diagonal Padé Approximants. Constr Approx 53, 545–567 (2021). https://doi.org/10.1007/s00365-020-09525-y
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DOI: https://doi.org/10.1007/s00365-020-09525-y