{"paper":{"title":"Laplace operators on the cone of Radon measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Anatoly Vershik, Eugene Lytvynov, Yuri Kondratiev","submitted_at":"2015-03-02T21:21:50Z","abstract_excerpt":"We consider the infinite-dimensional Lie group $\\mathfrak G$ which is the semidirect product of the group of compactly supported diffeomorphisms of a Riemannian manifold $X$ and the commutative multiplicative group of functions on $X$. The group $\\mathfrak G$ naturally acts on the space $\\mathbb M(X)$ of Radon measures on $X$. We would like to define a Laplace operator associated with a natural representation of $\\mathfrak G$ in $L^2(\\mathbb M(X),\\mu)$. Here $\\mu$ is assumed to be the law of a measure-valued L\\'evy process. A unitary representation of the group cannot be determined, since the "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1503.00750","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"}