Iterated convolutions and endless Riemann surfaces
| Autor: | David Sauzin, Shingo Kamimoto |
|---|---|
| Přispěvatelé: | Hiroshima University, Institut de Mécanique Céleste et de Calcul des Ephémérides (IMCCE), Institut national des sciences de l'Univers (INSU - CNRS)-Observatoire de Paris, Université Paris sciences et lettres (PSL)-Université Paris sciences et lettres (PSL)-Université de Lille-Sorbonne Université (SU)-Centre National de la Recherche Scientifique (CNRS), A*Midex Hypathie, ANR-12-BS01-0017,CARMA,Combinatoire Algébrique, Résurgence, Moules et Applications(2012), ANR-11-IDEX-0001,Amidex,INITIATIVE D'EXCELLENCE AIX MARSEILLE UNIVERSITE(2011) |
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Power series
Pure mathematics [MATH.MATH-DS]Mathematics [math]/Dynamical Systems [math.DS] Holomorphic function Dynamical Systems (math.DS) 01 natural sciences Theoretical Computer Science Convolution symbols.namesake Mathematics (miscellaneous) 0103 physical sciences FOS: Mathematics 0101 mathematics Mathematics - Dynamical Systems Mathematics Series (mathematics) Analytic continuation Riemann surface 010102 general mathematics Substitution (algebra) MSC: 34M30 40G10 30B40 convolution product analytic continuation Iterated function symbols 010307 mathematical physics resurgence theory |
| Zdroj: | Annali della Scuola Normale Superiore di Pisa, Classe di Scienze Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, Scuola Normale Superiore 2020, 20 (1), pp.177-215. ⟨10.2422/2036-2145.201708_008⟩ Annali della Scuola Normale Superiore di Pisa, Classe di Scienze, 2020, 20 (1), pp.177-215. ⟨10.2422/2036-2145.201708_008⟩ |
| ISSN: | 0391-173X 2036-2145 |
| DOI: | 10.2422/2036-2145.201708_008⟩ |
| Popis: | We discuss a version of \'Ecalle's definition of resurgence, based on the notion of endless continuability in the Borel plane. We relate this with the notion of \Omega-continuability, where \Omega\ is a discrete filtered set, and show how to construct a universal Riemann surface X_\Omega\ whose holomorphic functions are in one-to-one correspondence with \Omega-continuable functions. We then discuss the \Omega-continuability of convolution products and give estimates for iterated convolutions of the form \hat\phi_1*\cdots *\hat\phi_n. This allows us to handle nonlinear operations with resurgent series, e.g. substitution into a convergent power series. Comment: 32 pages, 4 figures |
| Databáze: | OpenAIRE |
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