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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1405.1276","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2014-05-06T14:05:36Z","cross_cats_sorted":[],"title_canon_sha256":"70cd8835ec71c23df7ebe6229b973758edc6be2ebe2d42533c2f65c4596c7315","abstract_canon_sha256":"c409ceb28ba14447722a47ca274a210741fe2d8bdcb2cb3678a674346a338941"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:45:23.047505Z","signature_b64":"OAx27iCr4E7w6eB4SShgXj1HjUVFu5/09Yf3fqD8GkAxzK66qk9VnVAWNQuO3oouQP/0Yv1wMayXIBOvdEu2DA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"dcfd190863c339e86f4dbfd4c6c30ae0dc4d13da4bfabf8df5b547be94edb662","last_reissued_at":"2026-05-18T02:45:23.046948Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:45:23.046948Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $E_{2}$. 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