{"paper":{"title":"Coxeter system of planes are sets of injectivity for the twisted spherical means on $\\mathbb C^n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"R. K. Srivastava","submitted_at":"2012-04-12T17:14:14Z","abstract_excerpt":"In this article, we prove that any pair of perpendicular planes is a set of injectivity for the twisted spherical means (TSM) for $L^p(\\mathbb C^n) (n\\geq2)$ with $1\\leq p\\leq2.$ Then, we imitate that any Coxeter system of even number of planes is a set of injectivity for the TSM for $L^p(\\mathbb C^n).$ We further observe that a set $S_R^{2n-1}\\times\\mathbb C$ is a set of injectivity for the TSM for a ceratin class of functions on $\\mathbb C^{n+1}.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1204.2773","kind":"arxiv","version":4},"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"}