{"paper":{"title":"(Discrete) Almansi Type Decompositions: An umbral calculus framework based on $\\mathfrak{osp}(1|2)$ symmetries","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CV","authors_text":"Guangbin Ren, Nelson Faustino","submitted_at":"2011-02-26T18:35:43Z","abstract_excerpt":"We introduce the umbral calculus formalism for hypercomplex variables starting from the fact that the algebra of multivariate polynomials $\\BR[\\underline{x}]$ shall be described in terms of the generators of the Weyl-Heisenberg algebra. The extension of $\\BR[\\underline{x}]$ to the algebra of Clifford-valued polynomials $\\mathcal{P}$ gives rise to an algebra of Clifford-valued operators whose canonical generators are isomorphic to the orthosymplectic Lie algebra $\\mathfrak{osp}(1|2)$.\n  This extension provides an effective framework in continuity and discreteness that allow us to establish an a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1102.5434","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"}