{"paper":{"title":"Iterated convolutions and endless Riemann surfaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"David Sauzin, Shingo Kamimoto","submitted_at":"2016-10-18T06:56:31Z","abstract_excerpt":"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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.05453","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}