{"paper":{"title":"Pointwise convergence of solutions of the Schr\\\"odinger equation along general curves on Damek-Ricci spaces","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Utsav Dewan","submitted_at":"2024-11-21T11:04:54Z","abstract_excerpt":"One of the most celebrated problems in Euclidean Harmonic analysis is the Carleson's problem: determining the optimal regularity of the initial condition $f$ of the Schr\\\"odinger equation given by \\begin{equation*} \\begin{cases}\n  i\\frac{\\partial u}{\\partial t} =\\Delta u\\:,\\: (x,t) \\in \\mathbb{R}^n \\times \\mathbb{R} \\newline\n  u(0,\\cdot)=f\\:, \\text{ on } \\mathbb{R}^n \\:,\n  \\end{cases} \\end{equation*} in terms of the index $\\beta$ such that $f$ belongs to the inhomogeneous Sobolev space $H^\\beta(\\mathbb{R}^n)$, so that the solution of the Schr\\\"odinger operator $u$ converges pointwise to $f$, \\"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2411.14020","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/2411.14020/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"}