- 著者
- David Sauzin
- 出版者
- Division of Functional Equations, The Mathematical Society of Japan
- 雑誌
- Funkcialaj Ekvacioj (ISSN:05328721)
- 巻号頁・発行日
- vol.56, no.3, pp.397-413, 2013 (Released:2013-12-19)
- 参考文献数
- 11
- 被引用文献数
- 3 7
This article introduces, for any closed discrete subset Ω of C, the definition of Ω-continuability, a particular case of Écalle's resurgence: Ω-continuable functions are required to be holomorphic near 0 and to admit analytic continuation along any path which avoids Ω. We give a rigorous and self-contained treatment of the stability under convolution of this space of functions, showing that a necessary and sufficient condition is the stability of Ω under addition.