{"paper":{"title":"Global in time Strichartz estimates for the fractional Schr\\\"odinger equations on asymptotically Euclidean manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Van Duong Dinh","submitted_at":"2017-05-11T23:45:07Z","abstract_excerpt":"In this paper, we prove global in time Strichartz estimates for the fractional Schr\\\"odinger operators, namely $e^{-it\\Lambda_g^\\sigma}$ with $\\sigma \\in (0,\\infty)\\backslash \\{1\\}$ and $\\Lambda_g:=\\sqrt{-\\Delta_g}$ where $\\Delta_g$ is the Laplace-Beltrami operator on asymptotically Euclidean manifolds $(\\mathbb{R}^d,g)$. Let $f_0\\in C^\\infty_0(\\mathbb{R})$ be a smooth cutoff equal 1 near zero. We firstly show that the high frequency part $(1-f_0)(P)e^{-it\\Lambda_g^\\sigma}$ satisfies global in time Strichartz estimates as on $\\mathbb{R}^d$ of dimension $d\\geq 2$ inside a compact set under non-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04403","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":""},"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"}