{"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 $\\lambda(\\phi)=\\ln r(\\phi)$ ($\\phi\\in L$). In this manner we generalize to the infinite case Theorem 3.1 from \\cite{OZ1}."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.4962","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"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"}