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The Umbral Clifford analysis provides an effective framework in continuity and discreteness.\n  In this paper we consider functions defined in a star-like domain $\\Omega \\subset \\BR^n$ with values in the Umbral Clifford algebra $C\\ell_{0,n}'$ which are Umbral polymonogenic with respect to the (left) Umbral Dirac operator $D'$, i.e. they belong to the kernel of $(D')^k$. We prove that any polymonogenic function $f$ has a decomposition of the fo"},"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":"0901.4691","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2009-01-29T14:40:58Z","cross_cats_sorted":["math-ph","math.MP"],"title_canon_sha256":"83b2551ba51fded6e1d73c432095354961c5c490a5c34a230881e974f8afe61f","abstract_canon_sha256":"74c3b3b46a47e7b2e48a3b83a433a2939429357a77b121346ad301d367cb71e0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T04:27:45.625242Z","signature_b64":"aldf5/Gjv+TFAN6MtimE6JKLnquHZFEDPSV3c8d7lVau870PomETZ/fAAi2DI+szkHOXa3KmDDq/J/gC0Mb6CQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"349f61294930aa406fc657aa7fd12477b3f13700a67d8439d79431b7b317814a","last_reissued_at":"2026-05-18T04:27:45.624617Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T04:27:45.624617Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Almansi Theorems in Umbral Clifford Analysis and the Quantum Harmonic Oscillator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.CA","authors_text":"Guangbin Ren, Nelson Faustino","submitted_at":"2009-01-29T14:40:58Z","abstract_excerpt":"We introduce the Umbral calculus into Clifford analysis starting from the abstract of the Heisenberg commutation relation $[\\frac{d}{dx}, x] = {\\bf id}$. 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