{"bundle_type":"pith_open_graph_bundle","bundle_version":"1.0","pith_number":"pith:2018:3HBBAQSC5GZ2INNUYY5R3IHUGS","short_pith_number":"pith:3HBBAQSC","canonical_record":{"source":{"id":"1807.08557","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-07-23T12:20:35Z","cross_cats_sorted":[],"title_canon_sha256":"d7c5925eac64b20e27624dd16ed77ff12f158e630c0913469f40974e1995fe89","abstract_canon_sha256":"ff027b0f9c5623fcf6eae2bdbc18bad161107e27beea0e94611735d8e0804fe6"},"schema_version":"1.0"},"canonical_sha256":"d9c2104242e9b3a435b4c63b1da0f434973cd0ac4d22ce6b9b922538cf74babf","source":{"kind":"arxiv","id":"1807.08557","version":2},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.08557","created_at":"2026-05-17T23:50:27Z"},{"alias_kind":"arxiv_version","alias_value":"1807.08557v2","created_at":"2026-05-17T23:50:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.08557","created_at":"2026-05-17T23:50:27Z"},{"alias_kind":"pith_short_12","alias_value":"3HBBAQSC5GZ2","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3HBBAQSC5GZ2INNU","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3HBBAQSC","created_at":"2026-05-18T12:32:02Z"}],"events":[{"event_type":"record_created","subject_pith_number":"pith:2018:3HBBAQSC5GZ2INNUYY5R3IHUGS","target":"record","payload":{"canonical_record":{"source":{"id":"1807.08557","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-07-23T12:20:35Z","cross_cats_sorted":[],"title_canon_sha256":"d7c5925eac64b20e27624dd16ed77ff12f158e630c0913469f40974e1995fe89","abstract_canon_sha256":"ff027b0f9c5623fcf6eae2bdbc18bad161107e27beea0e94611735d8e0804fe6"},"schema_version":"1.0"},"canonical_sha256":"d9c2104242e9b3a435b4c63b1da0f434973cd0ac4d22ce6b9b922538cf74babf","receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:50:27.497111Z","signature_b64":"1525tWI7WWnow0tjRDhkUtc7i1DqWUrjWLqQ9+dEgtKkCyvwYP+sbW3kKNIkqC4nwGnmCr4zevoALTQQZeOkCw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d9c2104242e9b3a435b4c63b1da0f434973cd0ac4d22ce6b9b922538cf74babf","last_reissued_at":"2026-05-17T23:50:27.496593Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:50:27.496593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"source_kind":"arxiv","source_id":"1807.08557","source_version":2,"attestation_state":"computed"},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:50:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"OIHXDuY9LAT/uQXNiZDt2IlLO/G/GlqSUSnJY+R4SnpGamU6ay2ONKbuj8Oh5Pbq0ZoNUt0NuURkWv4LqXX0AQ==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T20:48:19.108593Z"},"content_sha256":"60a24386498d12e3f00166fa75be23c398740f521200564b3e2466a940c4167e","schema_version":"1.0","event_id":"sha256:60a24386498d12e3f00166fa75be23c398740f521200564b3e2466a940c4167e"},{"event_type":"graph_snapshot","subject_pith_number":"pith:2018:3HBBAQSC5GZ2INNUYY5R3IHUGS","target":"graph","payload":{"graph_snapshot":{"paper":{"title":"Power bounded weighted composition operators on function spaces defined by local properties","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Thomas Kalmes","submitted_at":"2018-07-23T12:20:35Z","abstract_excerpt":"We study power boundedness and related properties such as mean ergodicity for (weighted) composition operators on function spaces defined by local properties. As a main application of our general approach we characterize when (weighted) composition operators are power bounded, topologizable, and (uniformly) mean ergodic on kernels of certain linear partial differential operators including elliptic operators as well as non-degenrate parabolic operators. Moreover, under mild assumptions on the weight and the symbol we give a characterisation of those weighted composition operators on the Fr\\'ech"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08557","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"},"verdict_id":null},"signer":{"signer_id":"pith.science","signer_type":"pith_registry","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"created_at":"2026-05-17T23:50:27Z","supersedes":[],"prev_event":null,"signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"y3gEbhNfq0I1cTpjv8XxnOgPw0P5rZAk4nYTABc9KMoRP4sPNntylUy4oKIIoKYx955EMNeEh1Nkh9WeDkGsBg==","signed_message":"open_graph_event_sha256_bytes","signed_at":"2026-06-03T20:48:19.109148Z"},"content_sha256":"cf40edfc4f9260cfc28bc6399710a731169a64e3045027aa2ea6621565e1346c","schema_version":"1.0","event_id":"sha256:cf40edfc4f9260cfc28bc6399710a731169a64e3045027aa2ea6621565e1346c"}],"timestamp_proofs":[],"mirror_hints":[{"mirror_type":"https","name":"Pith Resolver","base_url":"https://pith.science","bundle_url":"https://pith.science/pith/3HBBAQSC5GZ2INNUYY5R3IHUGS/bundle.json","state_url":"https://pith.science/pith/3HBBAQSC5GZ2INNUYY5R3IHUGS/state.json","well_known_bundle_url":"https://pith.science/.well-known/pith/3HBBAQSC5GZ2INNUYY5R3IHUGS/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":"2026-06-03T20:48:19Z","links":{"resolver":"https://pith.science/pith/3HBBAQSC5GZ2INNUYY5R3IHUGS","bundle":"https://pith.science/pith/3HBBAQSC5GZ2INNUYY5R3IHUGS/bundle.json","state":"https://pith.science/pith/3HBBAQSC5GZ2INNUYY5R3IHUGS/state.json","well_known_bundle":"https://pith.science/.well-known/pith/3HBBAQSC5GZ2INNUYY5R3IHUGS/bundle.json"},"state":{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2018:3HBBAQSC5GZ2INNUYY5R3IHUGS","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":"ff027b0f9c5623fcf6eae2bdbc18bad161107e27beea0e94611735d8e0804fe6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-07-23T12:20:35Z","title_canon_sha256":"d7c5925eac64b20e27624dd16ed77ff12f158e630c0913469f40974e1995fe89"},"schema_version":"1.0","source":{"id":"1807.08557","kind":"arxiv","version":2}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1807.08557","created_at":"2026-05-17T23:50:27Z"},{"alias_kind":"arxiv_version","alias_value":"1807.08557v2","created_at":"2026-05-17T23:50:27Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1807.08557","created_at":"2026-05-17T23:50:27Z"},{"alias_kind":"pith_short_12","alias_value":"3HBBAQSC5GZ2","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_16","alias_value":"3HBBAQSC5GZ2INNU","created_at":"2026-05-18T12:32:02Z"},{"alias_kind":"pith_short_8","alias_value":"3HBBAQSC","created_at":"2026-05-18T12:32:02Z"}],"graph_snapshots":[{"event_id":"sha256:cf40edfc4f9260cfc28bc6399710a731169a64e3045027aa2ea6621565e1346c","target":"graph","created_at":"2026-05-17T23:50:27Z","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 power boundedness and related properties such as mean ergodicity for (weighted) composition operators on function spaces defined by local properties. As a main application of our general approach we characterize when (weighted) composition operators are power bounded, topologizable, and (uniformly) mean ergodic on kernels of certain linear partial differential operators including elliptic operators as well as non-degenrate parabolic operators. Moreover, under mild assumptions on the weight and the symbol we give a characterisation of those weighted composition operators on the Fr\\'ech","authors_text":"Thomas Kalmes","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-07-23T12:20:35Z","title":"Power bounded weighted composition operators on function spaces defined by local properties"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1807.08557","kind":"arxiv","version":2},"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":"sha256:60a24386498d12e3f00166fa75be23c398740f521200564b3e2466a940c4167e","target":"record","created_at":"2026-05-17T23:50:27Z","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":"ff027b0f9c5623fcf6eae2bdbc18bad161107e27beea0e94611735d8e0804fe6","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-07-23T12:20:35Z","title_canon_sha256":"d7c5925eac64b20e27624dd16ed77ff12f158e630c0913469f40974e1995fe89"},"schema_version":"1.0","source":{"id":"1807.08557","kind":"arxiv","version":2}},"canonical_sha256":"d9c2104242e9b3a435b4c63b1da0f434973cd0ac4d22ce6b9b922538cf74babf","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"d9c2104242e9b3a435b4c63b1da0f434973cd0ac4d22ce6b9b922538cf74babf","first_computed_at":"2026-05-17T23:50:27.496593Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-17T23:50:27.496593Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"1525tWI7WWnow0tjRDhkUtc7i1DqWUrjWLqQ9+dEgtKkCyvwYP+sbW3kKNIkqC4nwGnmCr4zevoALTQQZeOkCw==","signature_status":"signed_v1","signed_at":"2026-05-17T23:50:27.497111Z","signed_message":"canonical_sha256_bytes"},"source_id":"1807.08557","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:60a24386498d12e3f00166fa75be23c398740f521200564b3e2466a940c4167e","sha256:cf40edfc4f9260cfc28bc6399710a731169a64e3045027aa2ea6621565e1346c"],"state_sha256":"163f8c632756394a3d357adba9b54d56290db1effd86f3cf8f2f9f63d4888aa9"},"bundle_signature":{"signature_status":"signed_v1","algorithm":"ed25519","key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signature_b64":"U1Fh9laMA+JH14fVsggWFn0tzf24Yuc0Y9vW5TeFKK0kXhrrgBeSmCtlO/hW2tr57Lognp8VopK309w+xXQ6CQ==","signed_message":"bundle_sha256_bytes","signed_at":"2026-06-03T20:48:19.111783Z","bundle_sha256":"3a8d9e458e33ec909f8929fb0f491ab7602fd40f6efc123d352eb9d8031ab13d"}}