{"paper":{"title":"Estimates for Nonlinear Harmonic Measures on Trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Carolina A. Mosquera, Julio D. Rossi, Leandro M. Del Pezzo","submitted_at":"2013-03-26T15:14:41Z","abstract_excerpt":"In this paper we give some estimates for nonlinear harmonic measures on trees. In particular, we estimate in terms of the size of a set $D$ the value at the origin of the solution to $\nu(x)=F((x,0),\\dots,(x,m-1))$ for every $x\\in\\mathbb{T}_m, $ a directed tree with $m$ branches with initial datum $f+\\chi_D$. Here $F$ is an averaging operator on $\\mathbb{R}^m$, $x$ is a vertex of a directed tree $\\mathbb{T}_m$ with regular $m$-branching and $(x,i)$ denotes a successor of that vertex for $0\\le i\\le m-1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.6521","kind":"arxiv","version":2},"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"}