{"paper":{"title":"The quantitative isoperimetric inequality for the Hilbert-Schmidt norm of localization operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Fabio Nicola, Federico Riccardi","submitted_at":"2024-01-09T16:29:57Z","abstract_excerpt":"In this paper we study the Hilbert-Schmidt norm of time-frequency localization operators $L_{\\Omega} \\colon L^2(\\mathbb{R}^d) \\rightarrow L^2(\\mathbb{R}^d)$, with Gaussian window, associated with a subset $\\Omega\\subset\\mathbb{R}^{2d}$ of finite measure. We prove, in particular, that the Hilbert-Schmidt norm of $L_\\Omega$ is maximized, among all subsets $\\Omega$ of a given finite measure, when $\\Omega$ is a ball and that there are no other extremizers. Actually, the main result is a quantitative version of this estimate, with sharp exponent. A similar problem is addressed for wavelet localizat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2401.04659","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/2401.04659/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"}