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Here $\\delta$ is the Laguerre exterior differentiation operator, defined as the classical exterior differential, except that the partial derivatives $\\partial_{x_i}$ are replaced by the \"Laguerre derivatives\" $\\sqrt{x_i}\\partial_{x_i}$, and $\\delta^*$ is the adjoint of $\\delta$ with respect to inner product on forms defined by the Euclidean structure and the Laguerre measure $\\mu_\\alpha$. We prove d"},"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":"1407.2838","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2014-07-10T16:01:25Z","cross_cats_sorted":[],"title_canon_sha256":"e40377863d4e0ede4cbc75e3ae2ed85ff389d0b06daef161543b2397154f9642","abstract_canon_sha256":"7415734565ce3e357d752374ef3e2de12b74d88b54df3d88b25d6c418cb27633"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T02:47:53.548788Z","signature_b64":"RORRrLy/vIJgVUqPnK6i2xabFEFvsLc2cdQns3HDyu6skYgqqxEWZAf28ZxjyUt3Irp42HlF/ig+QDDbJoD5BQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"79a0c1ec4ae2dbd2db3f8a47b4726533fea3a94da226937c728712a0285d19cf","last_reissued_at":"2026-05-18T02:47:53.548172Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T02:47:53.548172Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Riesz Transforms and Spectral Multipliers of the Hodge-Laguerre Operator","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"G. Mauceri, M. Spinelli","submitted_at":"2014-07-10T16:01:25Z","abstract_excerpt":"On $\\mathbb{R}^d_+$, endowed with the Laguerre probability measure $\\mu_\\alpha$, we define a Hodge-Laguerre operator $\\mathbb{L}_\\alpha=\\delta\\delta^*+\\delta^* \\delta$ acting on differential forms. Here $\\delta$ is the Laguerre exterior differentiation operator, defined as the classical exterior differential, except that the partial derivatives $\\partial_{x_i}$ are replaced by the \"Laguerre derivatives\" $\\sqrt{x_i}\\partial_{x_i}$, and $\\delta^*$ is the adjoint of $\\delta$ with respect to inner product on forms defined by the Euclidean structure and the Laguerre measure $\\mu_\\alpha$. 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