{"paper":{"title":"Invertible Complex Measures on Euclidean Spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Alexander Lindner, David Berger","submitted_at":"2025-06-10T17:41:40Z","abstract_excerpt":"In 1971 Taylor characterised all complex measures on $\\mathbb{R}$ that are invertible with respect to convolution as those which can be written in the form $\\delta_\\gamma \\ast \\sigma^{\\ast m} \\ast \\exp(\\nu)$ for some $\\gamma\\in \\mathbb{R}$, some complex measure $\\nu$, some $m\\in \\mathbb{Z}$ and a given fixed invertible finite signed measure $\\sigma$ (which has characteristic function $\\mathbb{R} \\ni z \\mapsto (1+i z)/(1-i z)$). We extend Taylor's result to complex measures on $\\mathbb{R}^n$. Somewhat surprisingly, the structure of invertible complex measures on $\\mathbb{R}^n$ is not much more "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.09012","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2506.09012/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}