{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:AOMJU4YW3EN6E4K75SREWVYHCQ","short_pith_number":"pith:AOMJU4YW","schema_version":"1.0","canonical_sha256":"03989a7316d91be2715feca24b57071413031869227d89e6a3c2612c4edd180e","source":{"kind":"arxiv","id":"1611.06380","version":2},"attestation_state":"computed","paper":{"title":"On the exponential of semi-infinite quasi-Toeplitz matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Beatrice Meini, Dario A. Bini","submitted_at":"2016-11-19T15:20:02Z","abstract_excerpt":"Let $a(z)=\\sum_{i\\in\\mathbb Z}a_iz^i$ be a complex valued function defined for $|z|=1$, such that $\\sum_{i\\in\\mathbb Z}|ia_i|<\\infty$, and let $E=(e_{i,j})_{i,j\\in\\mathbb {Z}^+}$ be such that $\\sum_{i,j\\in\\mathbb{Z}^+}|e_{i,j}|<\\infty$. A semi-infinite quasi-Toeplitz matrix is a matrix of the kind $A=T(a)+E$, where $T(a)=(t_{i,j})_{i,j\\in\\mathbb{Z}^+}$ is the semi-infinite Toeplitz matrix associated with the symbol $a(z)$, that is, $t_{i,j}=a_{j-i}$ for $i,j\\in\\mathbb Z^+$. We analyze theoretical and computational properties of the exponential of $A$. More specifically, it is shown that $\\exp("},"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":"1611.06380","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-19T15:20:02Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"2d6de8763bba3399d9accd9f8bc816f0b80d753f28fe5701b153b275e49e6878","abstract_canon_sha256":"3f4bc29278569876ef8218f6c0c0b86859ba0ca5ed9814d12dc0bc8dafb52449"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T18:10:16.663072Z","signature_b64":"58CQLyffFmf3u9L60RRMqecSQnesLwnNrQ4KyCbKl423ZchH9tbLEg0AV5rh605Q52Uhs2oO1qb6iz2LnAVKCA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"03989a7316d91be2715feca24b57071413031869227d89e6a3c2612c4edd180e","last_reissued_at":"2026-06-04T18:10:16.662650Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T18:10:16.662650Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the exponential of semi-infinite quasi-Toeplitz matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["cs.NA"],"primary_cat":"math.NA","authors_text":"Beatrice Meini, Dario A. Bini","submitted_at":"2016-11-19T15:20:02Z","abstract_excerpt":"Let $a(z)=\\sum_{i\\in\\mathbb Z}a_iz^i$ be a complex valued function defined for $|z|=1$, such that $\\sum_{i\\in\\mathbb Z}|ia_i|<\\infty$, and let $E=(e_{i,j})_{i,j\\in\\mathbb {Z}^+}$ be such that $\\sum_{i,j\\in\\mathbb{Z}^+}|e_{i,j}|<\\infty$. A semi-infinite quasi-Toeplitz matrix is a matrix of the kind $A=T(a)+E$, where $T(a)=(t_{i,j})_{i,j\\in\\mathbb{Z}^+}$ is the semi-infinite Toeplitz matrix associated with the symbol $a(z)$, that is, $t_{i,j}=a_{j-i}$ for $i,j\\in\\mathbb Z^+$. We analyze theoretical and computational properties of the exponential of $A$. More specifically, it is shown that $\\exp("},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.06380","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/1611.06380/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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":"1611.06380","created_at":"2026-06-04T18:10:16.662714+00:00"},{"alias_kind":"arxiv_version","alias_value":"1611.06380v2","created_at":"2026-06-04T18:10:16.662714+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1611.06380","created_at":"2026-06-04T18:10:16.662714+00:00"},{"alias_kind":"pith_short_12","alias_value":"AOMJU4YW3EN6","created_at":"2026-06-04T18:10:16.662714+00:00"},{"alias_kind":"pith_short_16","alias_value":"AOMJU4YW3EN6E4K7","created_at":"2026-06-04T18:10:16.662714+00:00"},{"alias_kind":"pith_short_8","alias_value":"AOMJU4YW","created_at":"2026-06-04T18:10:16.662714+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/AOMJU4YW3EN6E4K75SREWVYHCQ","json":"https://pith.science/pith/AOMJU4YW3EN6E4K75SREWVYHCQ.json","graph_json":"https://pith.science/api/pith-number/AOMJU4YW3EN6E4K75SREWVYHCQ/graph.json","events_json":"https://pith.science/api/pith-number/AOMJU4YW3EN6E4K75SREWVYHCQ/events.json","paper":"https://pith.science/paper/AOMJU4YW"},"agent_actions":{"view_html":"https://pith.science/pith/AOMJU4YW3EN6E4K75SREWVYHCQ","download_json":"https://pith.science/pith/AOMJU4YW3EN6E4K75SREWVYHCQ.json","view_paper":"https://pith.science/paper/AOMJU4YW","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1611.06380&json=true","fetch_graph":"https://pith.science/api/pith-number/AOMJU4YW3EN6E4K75SREWVYHCQ/graph.json","fetch_events":"https://pith.science/api/pith-number/AOMJU4YW3EN6E4K75SREWVYHCQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/AOMJU4YW3EN6E4K75SREWVYHCQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/AOMJU4YW3EN6E4K75SREWVYHCQ/action/storage_attestation","attest_author":"https://pith.science/pith/AOMJU4YW3EN6E4K75SREWVYHCQ/action/author_attestation","sign_citation":"https://pith.science/pith/AOMJU4YW3EN6E4K75SREWVYHCQ/action/citation_signature","submit_replication":"https://pith.science/pith/AOMJU4YW3EN6E4K75SREWVYHCQ/action/replication_record"}},"created_at":"2026-06-04T18:10:16.662714+00:00","updated_at":"2026-06-04T18:10:16.662714+00:00"}