{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2015:F6TBINSMQMKXZGOUG7RMXS76IN","short_pith_number":"pith:F6TBINSM","schema_version":"1.0","canonical_sha256":"2fa614364c83157c99d437e2cbcbfe434b32006f4a3e6604b2df715be248e0ef","source":{"kind":"arxiv","id":"1512.06883","version":2},"attestation_state":"computed","paper":{"title":"On Convolution Dominated Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Gero Fendler, Michael Leinert","submitted_at":"2015-12-14T11:34:31Z","abstract_excerpt":"For a locally compact group $G$ we consider the algebra $CD(G)$ of convolution dominated operators on $L^{2}(G)$: An operator $A:L^2(G)\\to L^2(G)$ is called convolution dominated if there exists $a\\in L^1(G)$ such that for all $f \\in L^2(G)$ $ |Af(x)| \\leq a * |f| (x)$, for almost all $x \\in G$.\n  In the case of discrete groups those operators can be dealt with quite sufficiently if the group in question is rigidly symmetric. For non-discrete groups we investigate the subalgebra of regular convolution dominated operators $CD_{reg}(G)$.\n  For amenable $G$ which is rigidly symmetric as a discret"},"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":"1512.06883","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2015-12-14T11:34:31Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"d8d9f9fb9b4b1dfd9457c11f47ceb1aa11dd5572e3359a08d20aab16ca454f7c","abstract_canon_sha256":"aca21d2dd283d6b94e249e4292b09d8ac5dccf40aafbf26c55ec739bbccead82"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:03:59.746622Z","signature_b64":"hSsQNX36iHPQ7/sWteT311ogbmagw/mCi6npTtf8LoYySJBTw/VPyzAzBFY9Y4m1V7BZuF6L50odKMcLcxKMAQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2fa614364c83157c99d437e2cbcbfe434b32006f4a3e6604b2df715be248e0ef","last_reissued_at":"2026-05-18T01:03:59.745976Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:03:59.745976Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Convolution Dominated Operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.FA","authors_text":"Gero Fendler, Michael Leinert","submitted_at":"2015-12-14T11:34:31Z","abstract_excerpt":"For a locally compact group $G$ we consider the algebra $CD(G)$ of convolution dominated operators on $L^{2}(G)$: An operator $A:L^2(G)\\to L^2(G)$ is called convolution dominated if there exists $a\\in L^1(G)$ such that for all $f \\in L^2(G)$ $ |Af(x)| \\leq a * |f| (x)$, for almost all $x \\in G$.\n  In the case of discrete groups those operators can be dealt with quite sufficiently if the group in question is rigidly symmetric. For non-discrete groups we investigate the subalgebra of regular convolution dominated operators $CD_{reg}(G)$.\n  For amenable $G$ which is rigidly symmetric as a discret"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.06883","kind":"arxiv","version":2},"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":"1512.06883","created_at":"2026-05-18T01:03:59.746074+00:00"},{"alias_kind":"arxiv_version","alias_value":"1512.06883v2","created_at":"2026-05-18T01:03:59.746074+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1512.06883","created_at":"2026-05-18T01:03:59.746074+00:00"},{"alias_kind":"pith_short_12","alias_value":"F6TBINSMQMKX","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_16","alias_value":"F6TBINSMQMKXZGOU","created_at":"2026-05-18T12:29:19.899920+00:00"},{"alias_kind":"pith_short_8","alias_value":"F6TBINSM","created_at":"2026-05-18T12:29:19.899920+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/F6TBINSMQMKXZGOUG7RMXS76IN","json":"https://pith.science/pith/F6TBINSMQMKXZGOUG7RMXS76IN.json","graph_json":"https://pith.science/api/pith-number/F6TBINSMQMKXZGOUG7RMXS76IN/graph.json","events_json":"https://pith.science/api/pith-number/F6TBINSMQMKXZGOUG7RMXS76IN/events.json","paper":"https://pith.science/paper/F6TBINSM"},"agent_actions":{"view_html":"https://pith.science/pith/F6TBINSMQMKXZGOUG7RMXS76IN","download_json":"https://pith.science/pith/F6TBINSMQMKXZGOUG7RMXS76IN.json","view_paper":"https://pith.science/paper/F6TBINSM","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1512.06883&json=true","fetch_graph":"https://pith.science/api/pith-number/F6TBINSMQMKXZGOUG7RMXS76IN/graph.json","fetch_events":"https://pith.science/api/pith-number/F6TBINSMQMKXZGOUG7RMXS76IN/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/F6TBINSMQMKXZGOUG7RMXS76IN/action/timestamp_anchor","attest_storage":"https://pith.science/pith/F6TBINSMQMKXZGOUG7RMXS76IN/action/storage_attestation","attest_author":"https://pith.science/pith/F6TBINSMQMKXZGOUG7RMXS76IN/action/author_attestation","sign_citation":"https://pith.science/pith/F6TBINSMQMKXZGOUG7RMXS76IN/action/citation_signature","submit_replication":"https://pith.science/pith/F6TBINSMQMKXZGOUG7RMXS76IN/action/replication_record"}},"created_at":"2026-05-18T01:03:59.746074+00:00","updated_at":"2026-05-18T01:03:59.746074+00:00"}