論文

査読有り
2015年

Irregular modified A-hypergeometric systems

Transactions of the American Mathematical Society
  • Francisco-Jesús Castro-Jiménez
  • ,
  • María-Cruz Fernández-Fernández
  • ,
  • Tatsuya Koike
  • ,
  • Nobuki Takayama

367
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&lt
sup&gt
w&lt
/sup&gt
·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.

リンク情報
DOI
https://doi.org/10.1090/S0002-9947-2014-06225-9
ID情報
  • DOI : 10.1090/S0002-9947-2014-06225-9
  • ISSN : 0002-9947
  • SCOPUS ID : 84929440301

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