2015年
Irregular modified A-hypergeometric systems
Transactions of the American Mathematical Society
- ,
- ,
- ,
- 巻
- 367
- 号
- 8
- 開始ページ
- 5415
- 終了ページ
- 5445
- 記述言語
- 英語
- 掲載種別
- 研究論文(学術雑誌)
- DOI
- 10.1090/S0002-9947-2014-06225-9
- 出版者・発行元
- American Mathematical Society
A modified A-hypergeometric system is a system of differential equations for the function f(t<
sup>
w<
/sup>
·x), where f(y) is a solution of an A-hypergeometric system in n variables and w is an n-dimensional integer vector, which is called the weight vector. We study the irregularity of modified systems by adapting to this case the notion of umbrella introduced by M. Schulze and U. Walther. Especially, we study slopes and Gevrey series solutions. We develop some applications of this study. Under some conditions we give Laplace integral representations of divergent series solutions of the modified system and we show that certain Gevrey series solutions of the original A-hypergeometric system along coordinate varieties are Gevrey asymptotic expansions of holomorphic solutions of the A-hypergeometric system.
sup>
w<
/sup>
·x), where f(y) is a solution of an A-hypergeometric system in n variables and w is an n-dimensional integer vector, which is called the weight vector. We study the irregularity of modified systems by adapting to this case the notion of umbrella introduced by M. Schulze and U. Walther. Especially, we study slopes and Gevrey series solutions. We develop some applications of this study. Under some conditions we give Laplace integral representations of divergent series solutions of the modified system and we show that certain Gevrey series solutions of the original A-hypergeometric system along coordinate varieties are Gevrey asymptotic expansions of holomorphic solutions of the A-hypergeometric system.
- ID情報
-
- DOI : 10.1090/S0002-9947-2014-06225-9
- ISSN : 0002-9947
- SCOPUS ID : 84929440301