{"paper":{"title":"Wavelet transform and Radon transform on the Quaternion Heisenberg group","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Heping Liu, JIanxun He","submitted_at":"2011-10-17T03:41:11Z","abstract_excerpt":"Let $\\mathscr Q$ be the quaternion Heisenberg group, and let $\\mathbf P$ be the affine automorphism group of $\\mathscr Q$. We develop the theory of continuous wavelet transform on the quaternion Heisenberg group via the unitary representations of $\\mathbf P$ on $L^2(\\mathscr Q)$. A class of radial wavelets is constructed. The inverse wavelet transform is simplified by using radial wavelets. Then we investigate the Radon transform on $\\mathscr Q$. A Semyanistri-Lizorkin space is introduced, on which the Radon transform is a bijection. We deal with the Radon transform on $\\mathscr Q$ both by the"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1110.3570","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"}