Multisummability for some classes of difference equations
Multisummability for some classes of difference equations
复制标题
某些类差分方程的多重可求性
DOI：
10.5802/aif.1511
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发表时间：
1996
期刊：
影响因子：
--
通讯作者：
B. F. Faber
中科院分区：
文献类型：
--
作者：
B. Braaksma;B. F. Faber
本文讨论差分方程组y(x+1)=G(x，y)，其中G取值于C-n中，G在x中为亚纯，在C中为无穷邻域，在C-n中为全纯。证明了在G的线性部分满足一定条件下，x(-1/p)中的形式幂级数解是可重和的，p是N的一个元素。此外，证明了形式解总是可以提升到上、下半平面上的全纯解，但这些解一般不是由形式解唯一决定的。
This paper concerns difference equations y(x + 1) = G(x, y) where G takes values in C-n and G is meromorphic in x in a neighborhood of infinity in C and holomorphic in a neighborhood of 0 in C-n. It is shown that under certain conditions on the linear part of G, formal power series solutions in x(-1/p),p is an element of N, are multisummable. Moreover, it is shown that formal solutions may always be lifted to holomorphic solutions in upper and lower halfplanes, but in general these solutions are not uniquely determined by the formal solutions.