{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2017:WO4OEUHNYOGCUF35KAQFBF3FGO","short_pith_number":"pith:WO4OEUHN","canonical_record":{"source":{"id":"1710.00891","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-10-02T20:13:06Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"52fd5df3f90d32ae7be4eef6831f3a27bbd3c1a8e6d412f16f7b10c5635f7789","abstract_canon_sha256":"a37d02e21d89ce4aaa2331d3b3d2ee6762a0d4459b525ec4fd7182e7af948193"},"schema_version":"1.0"},"canonical_sha256":"b3b8e250edc38c2a177d502050976533b64883c2e4f8c92e93d0f39d98d21521","source":{"kind":"arxiv","id":"1710.00891","version":3},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00891","created_at":"2026-05-18T00:04:13Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00891v3","created_at":"2026-05-18T00:04:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00891","created_at":"2026-05-18T00:04:13Z"},{"alias_kind":"pith_short_12","alias_value":"WO4OEUHNYOGC","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WO4OEUHNYOGCUF35","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WO4OEUHN","created_at":"2026-05-18T12:31:53Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2017:WO4OEUHNYOGCUF35KAQFBF3FGO","target":"record","payload":{"canonical_record":{"source":{"id":"1710.00891","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-10-02T20:13:06Z","cross_cats_sorted":["math.AP"],"title_canon_sha256":"52fd5df3f90d32ae7be4eef6831f3a27bbd3c1a8e6d412f16f7b10c5635f7789","abstract_canon_sha256":"a37d02e21d89ce4aaa2331d3b3d2ee6762a0d4459b525ec4fd7182e7af948193"},"schema_version":"1.0"},"canonical_sha256":"b3b8e250edc38c2a177d502050976533b64883c2e4f8c92e93d0f39d98d21521","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:04:13.568162Z","signature_b64":"UUX5clTbDWdG5zpZIaw6gcOUOjkUFGJ51BJ+8kLnYVyec9mC4V0u3tzHI974aBT9qsFEjpaK1cykI++XVrF/DQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"b3b8e250edc38c2a177d502050976533b64883c2e4f8c92e93d0f39d98d21521","last_reissued_at":"2026-05-18T00:04:13.567453Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:04:13.567453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1710.00891","source_version":3,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:04:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"Gx1/HTdzEcIQ6tiHz2kAsTfCwCULT4dk8egK2D9Y64MtGbBY+DrawxdkIdvEsZZinNO0YEWuwsDZJoLFm4NvBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T10:03:02.547473Z"},"content_sha256":"2386c5a196604dcfda89ab2acf3862d38e5fc510da0009bd6f31af8389aca25b","schema_version":"1.0","event_id":"sha256:2386c5a196604dcfda89ab2acf3862d38e5fc510da0009bd6f31af8389aca25b"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2017:WO4OEUHNYOGCUF35KAQFBF3FGO","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Stability theory for semigroups using $(L^{p},L^{q})$ Fourier multipliers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.FA","authors_text":"Jan Rozendaal, Mark Veraar","submitted_at":"2017-10-02T20:13:06Z","abstract_excerpt":"We study polynomial and exponential stability for $C_{0}$-semigroups using the recently developed theory of operator-valued $(L^{p},L^{q})$ Fourier multipliers. We characterize polynomial decay of orbits of a $C_{0}$-semigroup in terms of the $(L^{p},L^{q})$ Fourier multiplier properties of its resolvent. Using this characterization we derive new polynomial decay rates which depend on the geometry of the underlying space. We do not assume that the semigroup is uniformly bounded, our results depend only on spectral properties of the generator. As a corollary of our work on polynomial stability "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00891","kind":"arxiv","version":3},"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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-18T00:04:13Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"IgIvEUOi4dRzEcxpF1CjUMvD3yw0ZP6/ed1y2/a3stryypC6nzPsnNSGzOExOd1WLzAuY6qs/s/WyUxxFp3RDg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-25T10:03:02.547830Z"},"content_sha256":"f403a005121554f080be8d7d147aa01a6e83d71e832ef6186e2d9361b329447b","schema_version":"1.0","event_id":"sha256:f403a005121554f080be8d7d147aa01a6e83d71e832ef6186e2d9361b329447b"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/WO4OEUHNYOGCUF35KAQFBF3FGO/bundle.json","state_url":"https://pith.science/pith/WO4OEUHNYOGCUF35KAQFBF3FGO/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/WO4OEUHNYOGCUF35KAQFBF3FGO/bundle.json","status":"primary"}],"public_keys":[{"key_id":"pith-v1-2026-05","algorithm":"ed25519","format":"raw","public_key_b64":"stVStoiQhXFxp4s2pdzPNoqVNBMojDU/fJ2db5S3CbM=","public_key_hex":"b2d552b68890857171a78b36a5dccf368a953413288c353f7c9d9d6f94b709b3","fingerprint_sha256_b32_first128bits":"RVFV5Z2OI2J3ZUO7ERDEBCYNKS","fingerprint_sha256_hex":"8d4b5ee74e4693bcd1df2446408b0d54","rotates_at":null,"url":"https://pith.science/pith-signing-key.json","notes":"Pith uses this Ed25519 key to sign canonical record SHA-256 digests. Verify with: ed25519_verify(public_key, message=canonical_sha256_bytes, signature=base64decode(signature_b64))."}],"merge_version":"pith-open-graph-merge-v1","built_at":"2026-06-25T10:03:02Z","links":{"resolver":"https://pith.science/pith/WO4OEUHNYOGCUF35KAQFBF3FGO","bundle":"https://pith.science/pith/WO4OEUHNYOGCUF35KAQFBF3FGO/bundle.json","state":"https://pith.science/pith/WO4OEUHNYOGCUF35KAQFBF3FGO/state.json","well_known_bundle":"https://pith.science/.well-known/pith/WO4OEUHNYOGCUF35KAQFBF3FGO/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2017:WO4OEUHNYOGCUF35KAQFBF3FGO","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"a37d02e21d89ce4aaa2331d3b3d2ee6762a0d4459b525ec4fd7182e7af948193","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-10-02T20:13:06Z","title_canon_sha256":"52fd5df3f90d32ae7be4eef6831f3a27bbd3c1a8e6d412f16f7b10c5635f7789"},"schema_version":"1.0","source":{"id":"1710.00891","kind":"arxiv","version":3}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1710.00891","created_at":"2026-05-18T00:04:13Z"},{"alias_kind":"arxiv_version","alias_value":"1710.00891v3","created_at":"2026-05-18T00:04:13Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1710.00891","created_at":"2026-05-18T00:04:13Z"},{"alias_kind":"pith_short_12","alias_value":"WO4OEUHNYOGC","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_16","alias_value":"WO4OEUHNYOGCUF35","created_at":"2026-05-18T12:31:53Z"},{"alias_kind":"pith_short_8","alias_value":"WO4OEUHN","created_at":"2026-05-18T12:31:53Z"}],"graph_snapshots":[{"event_id":"sha256:f403a005121554f080be8d7d147aa01a6e83d71e832ef6186e2d9361b329447b","target":"graph","created_at":"2026-05-18T00:04:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"We study polynomial and exponential stability for $C_{0}$-semigroups using the recently developed theory of operator-valued $(L^{p},L^{q})$ Fourier multipliers. We characterize polynomial decay of orbits of a $C_{0}$-semigroup in terms of the $(L^{p},L^{q})$ Fourier multiplier properties of its resolvent. Using this characterization we derive new polynomial decay rates which depend on the geometry of the underlying space. We do not assume that the semigroup is uniformly bounded, our results depend only on spectral properties of the generator. As a corollary of our work on polynomial stability ","authors_text":"Jan Rozendaal, Mark Veraar","cross_cats":["math.AP"],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-10-02T20:13:06Z","title":"Stability theory for semigroups using $(L^{p},L^{q})$ Fourier multipliers"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.00891","kind":"arxiv","version":3},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:2386c5a196604dcfda89ab2acf3862d38e5fc510da0009bd6f31af8389aca25b","target":"record","created_at":"2026-05-18T00:04:13Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"a37d02e21d89ce4aaa2331d3b3d2ee6762a0d4459b525ec4fd7182e7af948193","cross_cats_sorted":["math.AP"],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2017-10-02T20:13:06Z","title_canon_sha256":"52fd5df3f90d32ae7be4eef6831f3a27bbd3c1a8e6d412f16f7b10c5635f7789"},"schema_version":"1.0","source":{"id":"1710.00891","kind":"arxiv","version":3}},"canonical_sha256":"b3b8e250edc38c2a177d502050976533b64883c2e4f8c92e93d0f39d98d21521","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"b3b8e250edc38c2a177d502050976533b64883c2e4f8c92e93d0f39d98d21521","first_computed_at":"2026-05-18T00:04:13.567453Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T00:04:13.567453Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"UUX5clTbDWdG5zpZIaw6gcOUOjkUFGJ51BJ+8kLnYVyec9mC4V0u3tzHI974aBT9qsFEjpaK1cykI++XVrF/DQ==","signature_status":"signed_v1","signed_at":"2026-05-18T00:04:13.568162Z","signed_message":"canonical_sha256_bytes"},"source_id":"1710.00891","source_kind":"arxiv","source_version":3}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:2386c5a196604dcfda89ab2acf3862d38e5fc510da0009bd6f31af8389aca25b","sha256:f403a005121554f080be8d7d147aa01a6e83d71e832ef6186e2d9361b329447b"],"state_sha256":"031f565a2f5ed4e4a5941dc2dcae8dd4a646064a1bd76aebbd51ffda70cdb7a5"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"dMf8oY/zUpf41is0OTZSZTh20uNyaGnrJNK1hKTG4JusQGFV1/GjRQ7j42tysIXAQOX5NReRr8xtD5ogV3QsDA==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-25T10:03:02.549757Z","bundle_sha256":"c15bb3a616d00ba7565f62855b36a1812d1e27c2000a1896150cd72a34bca1b5"}}