{"paper":{"title":"A sharp $k$-plane Strichartz inequality for the Schr\\\"odinger equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Jonathan Bennett, Marina Iliopoulou, Neal Bez, Susana Guti\\'errez, Taryn C. Flock","submitted_at":"2016-11-11T13:13:49Z","abstract_excerpt":"We prove that $$ \\|X(|u|^2)\\|_{L^3_{t,\\ell}}\\leq C\\|f\\|_{L^2(\\mathbb{R}^2)}^2, $$ where $u(x,t)$ is the solution to the linear time-dependent Schr\\\"odinger equation on $\\mathbb{R}^2$ with initial datum $f$, and $X$ is the (spatial) X-ray transform on $\\mathbb{R}^2$. In particular, we identify the best constant $C$ and show that a datum $f$ is an extremiser if and only if it is a gaussian. We also establish bounds of this type in higher dimensions $d$, where the X-ray transform is replaced by the $k$-plane transform for any $1\\leq k\\leq d-1$. In the process we obtain sharp $L^2(\\mu)$ bounds on "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.03692","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"}