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In this paper we derive a formula on the Legendre-Fenchel transform of a functional $\\hat{\\lambda}({\\bf c},\\phi)=\\ln f_{\\bf c}(e^{\\lambda(\\phi)})$, where $\\lambda(\\phi)=\\ln r(\\phi)$ ($\\phi\\in L$). In this manner we generalize to the infinite case Theorem 3.1 from \\cite{OZ1}."},"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":"1110.4962","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2011-10-22T09:39:12Z","cross_cats_sorted":[],"title_canon_sha256":"76bda6035f7e2781f3b9b7a242bb77ea07f066e5a45d21044daf5d12e3450986","abstract_canon_sha256":"fd92661ea9f9382ce9a98926242a1862a168e8d7b5d2552df775784bdb4d8ab6"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:21:21.741509Z","signature_b64":"yoGEPKjOIstugWJkU5rvp+SjB1O5kcgUQePBuoNDPcOfUNNdvSeVx3HKC99Nobbq1uoVQZwlo/DLg+V8OhLIAg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2feb946260ade00128e035c94e18518cce6af4d447c25fdbcfd59fab7189cefe","last_reissued_at":"2026-05-18T03:21:21.740875Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:21:21.740875Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Convex conjugates of analytic functions of logarithmically convex functionals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Krzysztof Zajkowski","submitted_at":"2011-10-22T09:39:12Z","abstract_excerpt":"Let $f_{\\bf c}(r)=\\sum_{n=0}^\\infty e^{c_n}r^n$ be an analytic function; ${\\bf c}=(c_n)\\in l_\\infty$. We assume that $r$ is some logarithmically convex and lower semicontinuous functional on a locally convex topological space $L$. In this paper we derive a formula on the Legendre-Fenchel transform of a functional $\\hat{\\lambda}({\\bf c},\\phi)=\\ln f_{\\bf c}(e^{\\lambda(\\phi)})$, where $\\lambda(\\phi)=\\ln r(\\phi)$ ($\\phi\\in L$). 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