{"paper":{"title":"On semigroups generated by sums of even powers of Dunkl operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Agnieszka Hejna, Jacek Dziuba\\'nski","submitted_at":"2019-05-17T15:59:11Z","abstract_excerpt":"On the Euclidean space $\\mathbb R^N$ equipped with a normalized root system $R$, a multiplicity function $k\\geq 0$, and the associated measure $dw(\\mathbf x)=\\prod_{\\alpha\\in R} |\\langle \\mathbf x,\\alpha\\rangle|^{k(\\alpha)}d\\mathbf x$ we consider the differential-difference operator $$L=(-1)^{\\ell+1} \\sum_{j=1}^m T_{\\zeta_j}^{2\\ell},$$ where $\\zeta_1,...,\\zeta_m$ are nonzero vectors in $\\mathbb R^N$, which span $\\mathbb R^N$, and $T_{\\zeta_j}$ are the Dunkl operators. The operator $L$ is essentially self-adjoint on $L^2(dw)$ and generates a semigroup $\\{S_t\\}_{t \\geq 0}$ of linear self-adjoint"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1905.07344","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"}