{"paper":{"title":"Integral Representations and Decompositions of Operator Monotone Functions on the Nonnegative Reals","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Pattrawut Chansangiam","submitted_at":"2013-04-30T09:51:25Z","abstract_excerpt":"In this paper, we show that there is a one-to-one correspondence between operator monotone functions on the nonnegative reals and finite Borel measures on the unit interval. This correspondence appears as an integral representation of special operator monotone functions $x \\mapsto 1\\,!_t\\,x$ for $t \\in [0,1]$ with respect to a finite Borel measure on $[0,1]$, here $!_t$ denotes the $t$-weighted harmonic mean. Hence such functions form building blocks for arbitrary operator monotone functions on the nonnegative reals. Moreover, we use this integral representation to decompose operator monotone "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1304.7936","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"}