{"paper":{"title":"Energy forms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Marcel Schmidt","submitted_at":"2017-03-15T02:09:34Z","abstract_excerpt":"In this thesis we study energy forms. These are quadratic forms on the space of real-valued measurable $m$-a.e. determined functions $$E:L^0(m) \\to [0,\\infty],$$ which assign to a measurable function $f$ its energy $E(f)$. Their two defining characteristics are a contraction property and some form of continuity. The contraction property demands that for each normal contraction $C:\\mathbb R \\to \\mathbb R$ the energy of a function $f$ satisfies $$E(C \\circ f) \\leq E(f).$$ This is an abstract formulation of the postulate that cutting off fluctuations of a function (which is thought to describe so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.04883","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"}