{"paper":{"title":"Schr\\\"odinger equation on Damek-Ricci spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.AP","authors_text":"Jean-Philippe Anker (MAPMO), Maria Vallarino, Vittoria Pierfelice (MAPMO)","submitted_at":"2010-10-11T15:29:30Z","abstract_excerpt":"In this paper we consider the Laplace-Beltrami operator \\Delta on Damek-Ricci spaces and derive pointwise estimates for the kernel of exp(\\tau \\Delta), when \\tau \\in C* with Re(\\tau) \\geq 0. When \\tau \\in iR*, we obtain in particular pointwise estimates of the Schr\\\"odinger kernel associated with \\Delta. We then prove Strichartz estimates for the Schr\\\"odinger equation, for a family of admissible pairs which is larger than in the Euclidean case. This extends the results obtained by Anker and Pierfelice on real hyperbolic spaces. As a further application, we study the dispersive properties of t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1010.2137","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"}