{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:P5IGH73U45LBXAK47M7S2HLNVY","short_pith_number":"pith:P5IGH73U","schema_version":"1.0","canonical_sha256":"7f5063ff74e7561b815cfb3f2d1d6dae36f268dde8356bc731f0f9318c72a5b2","source":{"kind":"arxiv","id":"1805.10048","version":1},"attestation_state":"computed","paper":{"title":"Chaotic behaviour of the Fourier multipliers on Riemannian symmetric spaces of noncompact type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Rudra P. Sarkar, Swagato K. Ray","submitted_at":"2018-05-25T09:02:47Z","abstract_excerpt":"Let $X$ be a Riemannian symmetric space of noncompact type and $T$ be a linear translation-invariant operator which is bounded on $L^p(X)$. We shall show that if $T$ is not a constant multiple of identity then there exist complex constants $z$ such that $zT$ is chaotic on $L^p(X)$ when $p$ is in the sharp range $2<p<\\infty$. This vastly generalizes the result that dynamics of the (perturbed) heat semigroup is chaotic on $X$ proved in [15, 17]."},"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":"1805.10048","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-05-25T09:02:47Z","cross_cats_sorted":[],"title_canon_sha256":"ef97bfca6f005ddb7f8ae7aa008b248e1a83a2891fe7cb95ba9140ecc0546ffc","abstract_canon_sha256":"26df679a537273dfeeb3ef61f03ed02470d3ac0d24b4e9cba853dafe30bca4f4"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:58.397694Z","signature_b64":"SFWjG3gO8VVcnNqa4ieJnwjbcvKhUxetAos6yROjlKDRHPoTeg8NMzNer+gO4FxzPwQYMsPyf3KafDY4IV10Cg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"7f5063ff74e7561b815cfb3f2d1d6dae36f268dde8356bc731f0f9318c72a5b2","last_reissued_at":"2026-05-18T00:14:58.396987Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:58.396987Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Chaotic behaviour of the Fourier multipliers on Riemannian symmetric spaces of noncompact type","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Rudra P. Sarkar, Swagato K. Ray","submitted_at":"2018-05-25T09:02:47Z","abstract_excerpt":"Let $X$ be a Riemannian symmetric space of noncompact type and $T$ be a linear translation-invariant operator which is bounded on $L^p(X)$. We shall show that if $T$ is not a constant multiple of identity then there exist complex constants $z$ such that $zT$ is chaotic on $L^p(X)$ when $p$ is in the sharp range $2<p<\\infty$. This vastly generalizes the result that dynamics of the (perturbed) heat semigroup is chaotic on $X$ proved in [15, 17]."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10048","kind":"arxiv","version":1},"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1805.10048","created_at":"2026-05-18T00:14:58.397098+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.10048v1","created_at":"2026-05-18T00:14:58.397098+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10048","created_at":"2026-05-18T00:14:58.397098+00:00"},{"alias_kind":"pith_short_12","alias_value":"P5IGH73U45LB","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_16","alias_value":"P5IGH73U45LBXAK4","created_at":"2026-05-18T12:32:43.782077+00:00"},{"alias_kind":"pith_short_8","alias_value":"P5IGH73U","created_at":"2026-05-18T12:32:43.782077+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/P5IGH73U45LBXAK47M7S2HLNVY","json":"https://pith.science/pith/P5IGH73U45LBXAK47M7S2HLNVY.json","graph_json":"https://pith.science/api/pith-number/P5IGH73U45LBXAK47M7S2HLNVY/graph.json","events_json":"https://pith.science/api/pith-number/P5IGH73U45LBXAK47M7S2HLNVY/events.json","paper":"https://pith.science/paper/P5IGH73U"},"agent_actions":{"view_html":"https://pith.science/pith/P5IGH73U45LBXAK47M7S2HLNVY","download_json":"https://pith.science/pith/P5IGH73U45LBXAK47M7S2HLNVY.json","view_paper":"https://pith.science/paper/P5IGH73U","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.10048&json=true","fetch_graph":"https://pith.science/api/pith-number/P5IGH73U45LBXAK47M7S2HLNVY/graph.json","fetch_events":"https://pith.science/api/pith-number/P5IGH73U45LBXAK47M7S2HLNVY/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/P5IGH73U45LBXAK47M7S2HLNVY/action/timestamp_anchor","attest_storage":"https://pith.science/pith/P5IGH73U45LBXAK47M7S2HLNVY/action/storage_attestation","attest_author":"https://pith.science/pith/P5IGH73U45LBXAK47M7S2HLNVY/action/author_attestation","sign_citation":"https://pith.science/pith/P5IGH73U45LBXAK47M7S2HLNVY/action/citation_signature","submit_replication":"https://pith.science/pith/P5IGH73U45LBXAK47M7S2HLNVY/action/replication_record"}},"created_at":"2026-05-18T00:14:58.397098+00:00","updated_at":"2026-05-18T00:14:58.397098+00:00"}