Convergence of diagonal Padé approximants for functions analytic near 0

Lubinsky, D. S.

doi:10.1090/S0002-9947-1995-1283557-3

Convergence of diagonal Padé approximants for functions analytic near $0$
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Trans. Amer. Math. Soc. 347 (1995), 3149-3157 Request permission

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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