{"paper":{"title":"Integration of Oscillatory and Subanalytic Functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.LO"],"primary_cat":"math.AG","authors_text":"Daniel J. Miller, Georges Comte, Jean-Philippe Rolin, Raf Cluckers, Tamara Servi","submitted_at":"2016-01-08T12:22:21Z","abstract_excerpt":"We prove the stability under integration and under Fourier transform of a concrete class of functions containing all globally subanalytic functions and their complex exponentials. This paper extends the investigation started in [J.-M. Lion, J.-P. Rolin: \"Volumes, feuilles de Rolle de feuilletages analytiques et th\\'eor\\`eme de Wilkie\" Ann. Fac. Sci. Toulouse Math. (6) 7 (1998), no. 1, 93-112] and [R. Cluckers, D. J. Miller: \"Stability under integration of sums of products of real globally subanalytic functions and their logarithms\" Duke Math. J. 156 (2011), no. 2, 311-348] to an enriched frame"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.01850","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"}