{"paper":{"title":"On the Radius of Analyticity of Solutions to the Cubic Szeg\\\"o Equation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Edriss S. Titi, Patrick Gerard, Yanqiu Guo","submitted_at":"2013-03-25T14:53:18Z","abstract_excerpt":"This paper is concerned with the cubic Szeg\\H{o} equation $$ i\\partial_t u=\\Pi(|u|^2 u), $$ defined on the $L^2$ Hardy space on the one-dimensional torus $\\mathbb T$, where $\\Pi: L^2(\\mathbb T)\\rightarrow L^2_+(\\mathbb T)$ is the Szeg\\H{o} projector onto the non-negative frequencies. For analytic initial data, it is shown that the solution remains spatial analytic for all time $t\\in (-\\infty,\\infty)$. In addition, we find a lower bound for the radius of analyticity of the solution. Our method involves energy-like estimates of the special Gevrey class of analytic functions based on the $\\ell^1$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6148","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"}