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Endless continuability and convolution product


We provide a rigorous analysis for the so-called endlessly continuable germs of holomorphic functions or in other words, the Ecalle's resurgent functions. We follow and complete an approach due to Pham, based on the notion of discrete filtered set and the associated Riemann surface defined as the space of convenient homotopy classes of paths. Our main contribution consists in a complete though simple proof of the stability under convolution product of the space of endlessly continuable germs.
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Dates and versions

hal-01071005 , version 1 (05-10-2014)
hal-01071005 , version 2 (26-03-2015)



Eric Delabaere, Yafei Ou. Endless continuability and convolution product. 2014. ⟨hal-01071005v2⟩
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