{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2025:TGWDH7PX3QAKOIO5KPKTLMCI3Y","short_pith_number":"pith:TGWDH7PX","schema_version":"1.0","canonical_sha256":"99ac33fdf7dc00a721dd53d535b048de22af5d0ac4581cc0bc727b4e49ff9b18","source":{"kind":"arxiv","id":"2503.13561","version":1},"attestation_state":"computed","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. 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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. 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