{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:6KHUL3ROL4ONB5ATTEMEX7CJEF","short_pith_number":"pith:6KHUL3RO","schema_version":"1.0","canonical_sha256":"f28f45ee2e5f1cd0f41399184bfc492162c2990a1051331da5e485c7f42c228f","source":{"kind":"arxiv","id":"1805.10779","version":1},"attestation_state":"computed","paper":{"title":"Dynamics of $L^p$ multipliers on harmonic manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Kingshook Biswas, Rudra P. Sarkar","submitted_at":"2018-05-28T05:49:53Z","abstract_excerpt":"Let $X$ be a complete, simply connected harmonic manifold with sectional curvatures $K$ satisfying $K \\leq -1$. In \\cite{biswas6}, a Fourier transform was defined for functions on $X$, and a Fourier inversion formula and Plancherel theorem were proved. We use the Fourier transform to investigate the dynamics on $L^p(X)$ for $p > 2$ of certain bounded linear operators $T : L^p(X) \\to L^p(X)$ which we call \"$L^p$-multipliers\" in accordance with standard terminology. These operators are required to preserve the subspace of $L^p$ radial functions. A notion of convolution with radial functions was "},"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":"1805.10779","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2018-05-28T05:49:53Z","cross_cats_sorted":[],"title_canon_sha256":"18c642ef5dfa461da131c050cac26fbeb89070a951e8cf7291f531e6f8808e3b","abstract_canon_sha256":"51a965271738dd088f74a14e74b9372f86768a3d797be645d0d9dbcd2e724770"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:14:51.464124Z","signature_b64":"Mamr32F89SR8JvJwFTsr7tbPFqywL4JRftLyRlwA0zlEomSt9sC75GWql7aWA/xzDm2AOam1ap6rVUhRxUubAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"f28f45ee2e5f1cd0f41399184bfc492162c2990a1051331da5e485c7f42c228f","last_reissued_at":"2026-05-18T00:14:51.463427Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:14:51.463427Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Dynamics of $L^p$ multipliers on harmonic manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.DS","authors_text":"Kingshook Biswas, Rudra P. Sarkar","submitted_at":"2018-05-28T05:49:53Z","abstract_excerpt":"Let $X$ be a complete, simply connected harmonic manifold with sectional curvatures $K$ satisfying $K \\leq -1$. In \\cite{biswas6}, a Fourier transform was defined for functions on $X$, and a Fourier inversion formula and Plancherel theorem were proved. We use the Fourier transform to investigate the dynamics on $L^p(X)$ for $p > 2$ of certain bounded linear operators $T : L^p(X) \\to L^p(X)$ which we call \"$L^p$-multipliers\" in accordance with standard terminology. These operators are required to preserve the subspace of $L^p$ radial functions. A notion of convolution with radial functions was "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1805.10779","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":"1805.10779","created_at":"2026-05-18T00:14:51.463536+00:00"},{"alias_kind":"arxiv_version","alias_value":"1805.10779v1","created_at":"2026-05-18T00:14:51.463536+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1805.10779","created_at":"2026-05-18T00:14:51.463536+00:00"},{"alias_kind":"pith_short_12","alias_value":"6KHUL3ROL4ON","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_16","alias_value":"6KHUL3ROL4ONB5AT","created_at":"2026-05-18T12:32:08.215937+00:00"},{"alias_kind":"pith_short_8","alias_value":"6KHUL3RO","created_at":"2026-05-18T12:32:08.215937+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/6KHUL3ROL4ONB5ATTEMEX7CJEF","json":"https://pith.science/pith/6KHUL3ROL4ONB5ATTEMEX7CJEF.json","graph_json":"https://pith.science/api/pith-number/6KHUL3ROL4ONB5ATTEMEX7CJEF/graph.json","events_json":"https://pith.science/api/pith-number/6KHUL3ROL4ONB5ATTEMEX7CJEF/events.json","paper":"https://pith.science/paper/6KHUL3RO"},"agent_actions":{"view_html":"https://pith.science/pith/6KHUL3ROL4ONB5ATTEMEX7CJEF","download_json":"https://pith.science/pith/6KHUL3ROL4ONB5ATTEMEX7CJEF.json","view_paper":"https://pith.science/paper/6KHUL3RO","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1805.10779&json=true","fetch_graph":"https://pith.science/api/pith-number/6KHUL3ROL4ONB5ATTEMEX7CJEF/graph.json","fetch_events":"https://pith.science/api/pith-number/6KHUL3ROL4ONB5ATTEMEX7CJEF/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/6KHUL3ROL4ONB5ATTEMEX7CJEF/action/timestamp_anchor","attest_storage":"https://pith.science/pith/6KHUL3ROL4ONB5ATTEMEX7CJEF/action/storage_attestation","attest_author":"https://pith.science/pith/6KHUL3ROL4ONB5ATTEMEX7CJEF/action/author_attestation","sign_citation":"https://pith.science/pith/6KHUL3ROL4ONB5ATTEMEX7CJEF/action/citation_signature","submit_replication":"https://pith.science/pith/6KHUL3ROL4ONB5ATTEMEX7CJEF/action/replication_record"}},"created_at":"2026-05-18T00:14:51.463536+00:00","updated_at":"2026-05-18T00:14:51.463536+00:00"}