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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 "},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1703.00295","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-03-01T13:43:07Z","cross_cats_sorted":[],"title_canon_sha256":"fd3f5b4a31d3dda3d7e4e72321d77c9b4009997a64cf9886c8a14bf541358626","abstract_canon_sha256":"740e9b0e8ee3155ae97120fa26fdecda6f52b69bdfde7d6e9e45e8be5b9a683b"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:32:11.479717Z","signature_b64":"hpgAD1+/RA9JVTbcXweIqqqnAL1hyZ01MPmEv4C+iEVadOrkYFghZEb8qC2gc/kB3h7ZakO56Z2VIuD5tTaiCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"6f8ab2775a36737d76d21c660e1a6c08d890380679671a4ba35e823e08ad3a46","last_reissued_at":"2026-05-18T00:32:11.479128Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:32:11.479128Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $d\\geq5$. 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