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We prove a geometric generalization in which the Laplacian on $\\RR^n$ is replaced by the Laplacian, plus suitable potential, on a nontrapping asymptotically conic manifold, which is the first time such a result has been proven in the variable coeff"},"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":"1012.3780","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2010-12-16T23:26:29Z","cross_cats_sorted":["math.CA","math.SP"],"title_canon_sha256":"182adf9497ff12db751d2cda8a1f0f8f35ea85827dd50e677b5ed995bcee6fb3","abstract_canon_sha256":"1d00e9d306c958988c7e546a0f623ccb297b6c5eedb58155e9be1dc54506245f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:56:36.414586Z","signature_b64":"VMok10Gl/PdCv3XBiVoLFWRtOBaPtsNKOb42TFtrWAbPCmOFltuwGXGKxUdezAoqeYjLeCP5VQbC50/r+BX9CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"544380a293556d2804feded82eb1bd6d6508b89ce3c878d8a93f3ba2d0c3251d","last_reissued_at":"2026-05-18T03:56:36.413710Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:56:36.413710Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Restriction and spectral multiplier theorems on asymptotically conic manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA","math.SP"],"primary_cat":"math.AP","authors_text":"Adam Sikora, Andrew Hassell, Colin Guillarmou","submitted_at":"2010-12-16T23:26:29Z","abstract_excerpt":"The classical Stein-Tomas restriction theorem is equivalent to the statement that the spectral measure $dE(\\lambda)$ of the square root of the Laplacian on $\\RR^n$ is bounded from $L^p(\\RR^n)$ to $L^{p'}(\\RR^n)$ for $1 \\leq p \\leq 2(n+1)/(n+3)$, where $p'$ is the conjugate exponent to $p$, with operator norm scaling as $\\lambda^{n(1/p - 1/p') - 1}$. 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