{"paper":{"title":"Complex powers of analytic functions and meromorphic renormalization in QFT","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Nguyen Viet Dang","submitted_at":"2015-03-03T16:25:38Z","abstract_excerpt":"In this article, we study functional analytic properties of the meromorphic families of distributions $(\\prod_{i=1}^p (f_j+i0)^{\\lambda_j})_{(\\lambda_1,\\dots,\\lambda_p) \\in \\mathbb{C}^p}$ using Hironaka's resolution of singularities, then using recent works on the decomposition of meromorphic germs with linear poles, we renormalize products of powers of analytic functions $\\prod_{i=1}^p(f_j+i0)^{k_j}, k_j \\in \\mathbb{Z}$ in the space of distributions. We also study microlocal properties of $(\\prod_{i=1}^p (f_j+i0)^{\\lambda_j})_{(\\lambda_1,\\dots,\\lambda_p)\\in\\mathbb{C}^p}$ and $\\prod_{i=1}^p (f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00995","kind":"arxiv","version":1},"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"}