{"paper":{"title":"The orthonormal Strichartz estimates and convergence problem of density functions related to $\\partial_{x}^{3}+\\partial_{x}^{-1}$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Wei Yan, Xiangqian Yan, Yongsheng Li","submitted_at":"2025-03-17T07:14:50Z","abstract_excerpt":"In this article, we investigate the orthonormal Strichartz estimates and the convergence\n  problem of the density function associated with $\\partial_{x}^{3}+\\partial_{x}^{-1}$. Firstly,\n  when $\\gamma_{0}\\in\\mathfrak{S}^{\\beta}(\\dot{H}^{s})$ with $\\frac{1}{4}\\leq s<\\frac{1}{2},\\,\n  0<\\alpha\\leq 1$, and $1\\leq\\beta<\\frac{\\alpha}{1-2s}$, we prove that\n  $\\lim\\limits_{t\\longrightarrow0}\\sum\\limits_{j=1}^{+\\infty}\\lambda_{j} \\left|e^{-t(\\partial_{x}^{3}+\\partial_{x}^{-1})}f_{j}\\right|^{2}=\\sum\\limits_{j=1}^{+\\infty}\\lambda_{j} \\left|f_{j}\\right|^{2}.$\n  This extends the Theorem 1.1 of Yan et al. ("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2503.13561","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2503.13561/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"}