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We study the C$^*$-algebra $\\mathcal{MC}_R$ generated by all multiplication operators by continuous functions in $C(J_R)$ and the composition operator $C_R$ induced by $R$ on $L^2(J_R, \\mu^L)$. We show that the C$^*$-algebra $\\mathcal{MC}_R$ is isomorphic to the C$^*$-algebra $\\mathcal{O}_R (J_R)$ associated with the complex dynamical system $\\{R^{\\circ n} \\}_{n=1} ^\\infty$."},"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":"1502.02093","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.OA","submitted_at":"2015-02-07T03:48:25Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"d6e7157b85eab889eb532032910b4311ba2954646ad2b6c2f8b25bc47bb91916","abstract_canon_sha256":"e09ceb2118185e8eb0acb9b1e08fd69f245c3dba477f6d4d808c631866bca1c7"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:27:49.986168Z","signature_b64":"SNnoxD0jpS6dpqJ7LXPql1qnbR7du7ij4WpZG7sV8V/jtcqv1ZvMcZXKq9xdeWBWPcMWybwy1LHHkqqbsgI3Cw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"08a0ca27546d82dbf86db11dcaf80d91962f84d0a48c66e47eef1615ba66b2f4","last_reissued_at":"2026-05-18T02:27:49.985761Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:27:49.985761Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"C*-algebras generated by multiplication operators and composition operators with rational symbol","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.OA","authors_text":"Hiroyasu Hamada","submitted_at":"2015-02-07T03:48:25Z","abstract_excerpt":"Let $R$ be a rational function of degree at least two, let $J_R$ be the Julia set of $R$ and let $\\mu^L$ be the Lyubich measure of $R$. 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