{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2013:TGHYMEM4MG37WVY37JPBSRSV2Z","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":"a7f303ae1553eaf6ba15490f92fb7b75c04df33d9fecda2950cbadfb4eac961f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-06-04T14:14:45Z","title_canon_sha256":"3afbeffba3f857ceb2889aeec10883d0c45f3ca1b1687f5e24c4e77e3090b937"},"schema_version":"1.0","source":{"id":"1306.0800","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1306.0800","created_at":"2026-05-18T03:21:44Z"},{"alias_kind":"arxiv_version","alias_value":"1306.0800v1","created_at":"2026-05-18T03:21:44Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1306.0800","created_at":"2026-05-18T03:21:44Z"},{"alias_kind":"pith_short_12","alias_value":"TGHYMEM4MG37","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_16","alias_value":"TGHYMEM4MG37WVY3","created_at":"2026-05-18T12:28:02Z"},{"alias_kind":"pith_short_8","alias_value":"TGHYMEM4","created_at":"2026-05-18T12:28:02Z"}],"graph_snapshots":[{"event_id":"sha256:fa2943f3fd69dea05851a6d52555d4f05e8dc71145fd997dad1f29f9659a653a","target":"graph","created_at":"2026-05-18T03:21:44Z","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":"Generalized $\\mathbf{m}$-Gelfand-Shilov-Roumieu vector spaces $\\mathcal{S}_{\\mathbf{m}}(\\mathbf{X})$ are introduced. Here $\\mathbf{m} = (m^{(1)},...,m^{(n)})$, $\\mathbf{X}=(X_{1},...,X_{n})$ and $m^{(1)},...,m^{(n)}$ are sequences of positive real numbers and $X_{1},...,X_{n}$ are operators in a Hilbert space. Conditions are given on the sequences $m^{(1)},...,m^{(n)}$ and on the operators $X_{1},...,X_{n}$ so that the equality $S_{\\mathbf{m}}(\\mathbf{X}) = S_{m^{(1)}}(X_{1})\\cap ... \\cap{S}_{m^{(n)}}(X_{n})$ is valid. As a corollary we obtain a new proof of a characterization theorem for clas","authors_text":"Mihai Pascu","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-06-04T14:14:45Z","title":"On the characterization of Gelfand-Shilov-Roumieu spaces"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.0800","kind":"arxiv","version":1},"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":"sha256:53c8f2ab650e0d6eb5d27a415fafbae524e65bee7d8c1d287392ef0bc478c2c0","target":"record","created_at":"2026-05-18T03:21:44Z","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":"a7f303ae1553eaf6ba15490f92fb7b75c04df33d9fecda2950cbadfb4eac961f","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2013-06-04T14:14:45Z","title_canon_sha256":"3afbeffba3f857ceb2889aeec10883d0c45f3ca1b1687f5e24c4e77e3090b937"},"schema_version":"1.0","source":{"id":"1306.0800","kind":"arxiv","version":1}},"canonical_sha256":"998f86119c61b7fb571bfa5e194655d6705a3fccf5dbf713d6a53e463d4bb67c","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"998f86119c61b7fb571bfa5e194655d6705a3fccf5dbf713d6a53e463d4bb67c","first_computed_at":"2026-05-18T03:21:44.927541Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T03:21:44.927541Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"TP3GHO2Pzf8g3YSyC8V1PhC9BW9oXu1adCQCKXWt6StGBB4qz/gFnGrNYh+ojrx+UTmgyn4addPNt0QoRbrDCw==","signature_status":"signed_v1","signed_at":"2026-05-18T03:21:44.928088Z","signed_message":"canonical_sha256_bytes"},"source_id":"1306.0800","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:53c8f2ab650e0d6eb5d27a415fafbae524e65bee7d8c1d287392ef0bc478c2c0","sha256:fa2943f3fd69dea05851a6d52555d4f05e8dc71145fd997dad1f29f9659a653a"],"state_sha256":"19d248ed440c293b21fdc8367d6c16038cd53620bd810c6ab0a16172300d6b52"}