{"paper":{"title":"Decay Estimates and Strichartz Estimates of Fourth-order Schr\\\"{o}dinger Operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Avy Soffer, Hongliang Feng, Xiaohua Yao","submitted_at":"2017-03-01T13:43:07Z","abstract_excerpt":"We study time decay estimates of the fourth-order Schr\\\"{o}dinger operator $H=(-\\Delta)^{2}+V(x)$ in $\\mathbb{R}^{d}$ for $d=3$ and $d\\geq5$. We analyze the low energy and high energy behaviour of resolvent $R(H; z)$, and then derive the Jensen-Kato dispersion decay estimate and local decay estimate for $e^{-itH}P_{ac}$ under suitable spectrum assumptions of $H$. Based on Jensen-Kato decay estimate and local decay estimate, we obtain the $L^1\\rightarrow L^{\\infty}$ estimate of $e^{-itH}P_{ac}$ in $3$-dimension by Ginibre argument, and also establish the endpoint global Strichartz estimates of "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.00295","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"}