{"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 $\\mu_\\alpha$. We prove d"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.2838","kind":"arxiv","version":1},"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"}