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

DOI:
https://doi.org/10.1090/S0002-9947-1995-1283557-3

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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Additional Information

DOI:
https://doi.org/10.1090/S0002-9947-1995-1283557-3

Keywords:
Padé approximants,
convergence of diagonal Padé approximants,
pole distribution

Article copyright:
© Copyright 1995
American Mathematical Society