{"paper":{"title":"On integrals over a convex set of the Wigner distribution","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.SP","authors_text":"B\\'erang\\`ere Delourme, Nicolas Lerner, Thomas Duyckaerts","submitted_at":"2019-01-22T11:11:58Z","abstract_excerpt":"We provide an example of a normalized $L^{2}(\\mathbb R)$ function $u$ such that its Wigner distribution $\\mathcal W(u,u)$ has an integral $>1$ on the square $[0,a]\\times[0,a]$ for a suitable choice of $a$. This provides a negative answer to a question raised by P. Flandrin in 1988. Our arguments are based upon the study of the Weyl quantization of the indicatrix of ${\\mathbb R_{+}\\times\\mathbb R_{+}}$ along with a precise numerical analysis of its discretization."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1901.07262","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"}