{"paper":{"title":"Partial Cosine-Funk Transforms at Poles of the $\\textrm{Cos}^\\lambda$ Transform on Grassmann Manifolds","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Adam Cross, Gestur \\'Olafsson","submitted_at":"2014-11-15T00:18:11Z","abstract_excerpt":"The cosine-$\\lambda$ transform, denoted $\\mathcal{C}^\\lambda$, is a family of integral transforms we can define on the sphere and on the Grassmann manifolds $\\textrm{Gr}(p, \\mathbb{K}^n) = \\textrm{SU}(n,\\mathbb{K})/\\text{S}(\\textrm{U}(p,\\mathbb{K}) \\times \\textrm{U}(n-p,\\mathbb{K}))$ where $\\mathbb{K}$ is $\\mathbb{R}$, $\\mathbb{C}$ or the skew field $\\mathbb{H}$ of quaternions. The family $\\mathcal{C}^\\lambda$ extends meromorphically in $\\lambda$ to the complex plane with poles at (among other values) $\\lambda =-1,\\ldots, -p$. In this paper we normalize $\\mathcal{C}^\\lambda$ and evaluate at th"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1411.4089","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"}