{"paper":{"title":"An alternative concept of Riesz energy of measures with application to generalized condensers","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.CA","authors_text":"Bent Fuglede, Natalia Zorii","submitted_at":"2018-03-28T17:57:27Z","abstract_excerpt":"In view of a recent example of a positive Radon measure $\\mu$ on a domain $D\\subset\\mathbb R^n$, $n\\geqslant3$, such that $\\mu$ is of finite energy $E_g(\\mu)$ relative to the $\\alpha$-Green kernel $g$ on $D$, though the energy of $\\mu-\\mu^{D^c}$ relative to the $\\alpha$-Riesz kernel $|x-y|^{\\alpha-n}$, $0<\\alpha\\leqslant2$, is not well defined (here $\\mu^{D^c}$ is the $\\alpha$-Riesz swept measure of $\\mu$ onto $D^c=\\mathbb R^n\\setminus D$), we propose a weaker concept of $\\alpha$-Riesz energy for which this defect has been removed. This concept is applied to the study of a minimum weak $\\alpha"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1803.11079","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"}