Endless continuability and convolution product

2014/10/05 by Éric Delabaere, Delabaere, Eric, Yafei Ou +1
Mathematics · #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology

paper · pdf · doi:10.48550/arxiv.1410.1200

openalex publication_date 2014/10/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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