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A quasi-Toeplitz matrix associated with the continuous symbol $a(z)$ is a matrix of the form $A=T(a)+E$ where $E=(e_{i,j})$, $\\sum_{i,j\\in\\mathbb Z^+}|e_{i,j}|<\\infty$, and is called a CQT-matrix. Given a function $f(x)$ and a CQT matrix $M$, we provide conditions under which $f(M)$ is well defined and "},"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":"1611.06406","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NA","submitted_at":"2016-11-19T18:20:15Z","cross_cats_sorted":["cs.NA"],"title_canon_sha256":"df60e525b68c5bbfefce10c5e778958b3c091378232794fa919016fe85ecf847","abstract_canon_sha256":"0b909d618866dad6b0f8bf87d8d496ae06438660dbdf970cd37ffdff46e13b8c"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-06-04T18:10:16.682870Z","signature_b64":"+I7BHFC4Wlhu0aUmR3opvDszOcawP5flzWoHiKVnQ8TcjbqeXeKiwka9iH2WioPolrnDKH+8622SYpVmdGBbAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"5ad2173fe201f06976d5d270adfc023bdd3818ef7f1dababc3e62d8d1d8bef33","last_reissued_at":"2026-06-04T18:10:16.682479Z","signature_status":"signed_v1","first_computed_at":"2026-06-04T18:10:16.682479Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Functions of 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, Stefano Massei","submitted_at":"2016-11-19T18:20:15Z","abstract_excerpt":"Let $a(z)=\\sum_{i\\in\\mathbb Z}a_iz^i$ be a complex valued continuous function, defined for $|z|=1$, such that $\\sum_{i=-\\infty}^{+\\infty}|ia_i|<\\infty$. Consider the semi-infinite Toeplitz matrix $T(a)=(t_{i,j})_{i,j\\in\\mathbb Z^+}$ associated with the symbol $a(z)$ such that $t_{i,j}=a_{j-i}$. A quasi-Toeplitz matrix associated with the continuous symbol $a(z)$ is a matrix of the form $A=T(a)+E$ where $E=(e_{i,j})$, $\\sum_{i,j\\in\\mathbb Z^+}|e_{i,j}|<\\infty$, and is called a CQT-matrix. 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