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Then we prove sharp $L^p\\to L^p$ frequency truncated estimates for the Schr\\\"odinger group $e^{itH}$ for $p\\in[p_0,p'_0]$. In particular, our results apply to every operator of the form $H=(i\\nabla+A)^2+V$, with a magnetic potential $A\\in L^2_{loc}(\\mathbb{R}^d,\\mathbb{R}^d)$ and an electric potential $V$ whose positive and negative parts are in the local Kato class and in the Kato class, resp"},"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":"1409.6853","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-09-24T08:10:59Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"8bc1062feb1796d06a2ab8bef42c4d5bb317d9071b5d22be1b74dbc3f19e4ec2","abstract_canon_sha256":"0e4b7b33e6f3eba2e9ec2413ef30b29012f7457931b208ec676d517d602f9db0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:27.918811Z","signature_b64":"1F7W2W9XAV4x75uvJqnkvkarKoxhUE2+WTGD2ZELA3f7DhYHoqOCCdfnche92HXU+4+/g/dSdntLDRYMwSXJDA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"97cd1dd2e8a485c2aad8c7da4e8da2ed0eeb00133f82bd29c1989d2dbfa88ac1","last_reissued_at":"2026-05-18T00:20:27.918309Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:27.918309Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Sharp $L^p$ estimates for Schr\\\"odinger groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Fabio Nicola, Piero D'Ancona","submitted_at":"2014-09-24T08:10:59Z","abstract_excerpt":"Consider a non-negative self-adjoint operator $H$ in $L^2(\\mathbb{R}^d)$. 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