{"paper":{"title":"Second quantisation for skew convolution products of infinitely divisible measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"David Applebaum, Jan van Neerven","submitted_at":"2014-05-06T14:05:36Z","abstract_excerpt":"Suppose $\\lambda_1$ and $\\lambda_2$ are infinitely divisible Radon measures on real Banach spaces $E_1$ and $E_2$, respectively and let $T:E_{1} \\rightarrow E_{2}$ be a Borel measurable mapping so that $T(\\lambda_1) * \\rho = \\lambda_2 $ for some Radon probability measure $\\rho$ on $E_{2}$. Extending previous results for the Gaussian and the Poissonian case, we study the problem of representing the `transition operator' $P_{T}:L^{p}(E_{2}, \\lambda_{2}) \\rightarrow L^{p}(E_{1}, \\lambda_{1})$ given by $$ P_{T}f(x) = \\int_{E_{2}}f(T(x) + y)d\\rho(y) %% d\\rho(y) instead of \\rho(dy) in order to unify"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.1276","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"}