{"paper":{"title":"Analyticity of extremisers to the Airy Strichartz inequality","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Dirk Hundertmark, Shuanglin Shao","submitted_at":"2010-12-29T22:11:36Z","abstract_excerpt":"We prove that there exists an extremal function to the Airy Strichartz inequality, $e^{-t\\partial_x^3}: L^2(\\mathbb{R})\\to L^8_{t,x}(\\mathbb{R}^2)$ by using the linear profile decomposition. Furthermore we show that, if $f$ is an extremiser, then $f$ is extremely fast decaying in Fourier space and so $f$ can be extended to be an entire function on the whole complex domain. The rapid decay of the Fourier transform of extremisers is established with a bootstrap argument which relies on a refined bilinear Airy Strichartz estimate and a weighted Strichartz inequality."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1101.0012","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":""},"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"}