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.
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