关于闭于行的经典Pade'逼近的超收敛性
On overconvergent subsequencs of closed to rows classical Pade' approximants
摘要：
设$f$是具有正收敛半径的幂级数。本文研究了与f有关的经典Pade逼近序列pi{n，m_n}的超收敛现象，其中m（n）<=m（n+1）<=m（n），m（n）= o（n/ \log n）. m（n）= 0（n），因为n趋于无穷大。推广了Hadamard和A. A. Ostrowski与过收敛Taylor多项式有关的结果以及G. Lo'pez Lagomasino和A. Ferna'ndes Infante关于Pade表的固定行的过收敛连续性。
英文摘要：
Let $f$ be a power series with positive radius of convergence. In the present paper, we study the phenomenon of overconvergence of sequences of classical Pade' approximants pi{n,m_n} associated with f, where m(n)<=m(n+1)<=m(n) and m(n) = o(n/\log n), resp. m(n) = 0(n) as n is going to infiity. We extend classical results by J. Hadamard and A. A. Ostrowski related to overconvergent Taylor polynomials, as well as results by G. Lo'pez Lagomasino and A. Ferna'ndes Infante concerning overconvergent subsequences of a fixed row of the Pade' table.
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