{"paper":{"title":"Regularity and pointwise convergence for dispersive equations with asymptotically concave phase on Damek-Ricci spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Utsav Dewan","submitted_at":"2025-06-01T07:48:31Z","abstract_excerpt":"We study the Carleson's problem on Damek-Ricci spaces $S$ for dispersive equations: \\begin{equation*} \\begin{cases}\n  i\\frac{\\partial u}{\\partial t} +\\Psi(\\sqrt{-\\mathcal{L}} )u=0\\:,\\: (x,t) \\in S \\times \\mathbb{R} \\:, \\\\ u(0,\\cdot)=f\\:,\\: \\text{ on } S \\:,\n  \\end{cases}\n  \\end{equation*} where $\\mathcal{L}= \\Delta$, the Laplace-Beltrami operator or $\\tilde{\\Delta}$, the shifted Laplace-Beltrami operator, so that the corresponding phase function $\\psi$ satisfies for some $a \\in (0,1)$, the large frequency asymptotic: \\begin{equation*} \\psi(\\lambda)=\\lambda^a + \\mathcal{O}(1)\\:,\\:\\: \\lambda \\gg"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2506.00881","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/2506.00881/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"}