{"paper":{"title":"On an analytic description of the $\\alpha$-cosine transform on real Grassmannians","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.MG","authors_text":"Dmitry Gourevitch, Semyon Alesker, Siddhartha Sahi","submitted_at":"2014-09-17T07:26:33Z","abstract_excerpt":"The goal of this paper is to describe the $\\alpha$-cosine transform on functions on a Grassmannian of $i$-planes in an $n$-dimensional real vector space. in analytic terms as explicitly as possible. We show that for all but finitely many complex $\\alpha$ the $\\alpha$-cosine transform is a composition of the $(\\alpha+2)$-cosine transform with an explicitly written (though complicated) O(n)-invariant differential operator. For all exceptional values of $\\alpha$ except one we interpret the $\\alpha$-cosine transform explicitly as either the Radon transform or composition of two Radon transforms. E"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.4882","kind":"arxiv","version":3},"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"}