{"paper":{"title":"Pluripotential Numerics","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Federico Piazzon","submitted_at":"2017-04-11T16:55:24Z","abstract_excerpt":"We introduce numerical methods for the approximation of the main (global) quantities in Pluripotential Theory as the \\emph{extremal plurisubharmonic function} $V_E^*$ of a compact $\\mathcal L$-regular set $E\\subset \\C^n$, its \\emph{transfinite diameter} $\\delta(E),$ and the \\emph{pluripotential equilibrium measure} $\\mu_E:=\\ddcn{V_E^*}.$\n  The methods rely on the computation of a \\emph{polynomial mesh} for $E$ and numerical orthonormalization of a suitable basis of polynomials. We prove the convergence of the approximation of $\\delta(E)$ and the uniform convergence of our approximation to $V_E"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1704.03411","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"}