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Convergence of diagonal Padé approximants for functions analytic near 0

Author: D. S. Lubinsky
Journal: Trans. Amer. Math. Soc. 347 (1995), 3149-3157
MSC: Primary 41A21; Secondary 30E10
MathSciNet review: 1283557
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Abstract: For functions analytic in a neighbourhood of 0, we show that at least for a subsequence of the diagonal Padé approximants, the point 0 attracts a zero proportion of the poles. The same is true for every "sufficiently dense" diagonal subsequence. Consequently these subsequences have a convergence in capacity type property, which is possibly the correct analogue of the Nuttall-Pommerenke theorem in this setting.

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Keywords: Padé approximants, convergence of diagonal Padé approximants, pole distribution
Article copyright: © Copyright 1995 American Mathematical Society