{"paper":{"title":"Form Inequalities for Symmetric Contraction Semigroups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR","math.SP"],"primary_cat":"math.FA","authors_text":"Markus Haase","submitted_at":"2015-03-10T13:17:35Z","abstract_excerpt":"Consider --- for the generator \\({-}A\\) of a symmetric contraction semigroup over some measure space $\\mathrm{X}$, $1\\le p < \\infty$, $q$ the dual exponent and given measurable functions $F_j,\\: G_j : \\mathbb{C}^d \\to \\mathbb{C}$ --- the statement: $$ \\mathrm{Re}\\, \\sum_{j=1}^m \\int_{\\mathrm{X}} A F_j(\\mathbf{f}) \\cdot G_j(\\mathbf{f}) \\,\\,\\ge \\,\\,0 $$ {\\em for all $\\mathbb{C}^d$-valued measurable functions $\\mathbf{f}$ on $\\mathrm{X}$ such that $F_j(\\mathbf{f}) \\in \\mathrm{dom}(A_p)$ and $G_j(\\mathbf{f}) \\in \\mathrm{L}^q(\\mathrm{X})$ for all $j$.}\n  It is shown that this statement is valid in "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.02895","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"}