{"paper":{"title":"The shifted wave equation on Damek--Ricci spaces and on homogeneous trees","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"math.AP","authors_text":"Alberto G. Setti, Emmanuel Pedon (LM-Reims), Jean-Philippe Anker (MAPMO), Pierre Martinot (IECN)","submitted_at":"2012-06-07T04:34:04Z","abstract_excerpt":"We solve explicitly the shifted wave equation on Damek--Ricci spaces, using Asgeirsson's theorem and the inverse dual Abel transform. As an application, we investigate Huygens' principle. A similar analysis is carried out in the discrete setting of homogeneous trees."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1206.1396","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"}