{"paper":{"title":"Spherical means in annular regions in the $n$-dimensional real hyperbolic spaces","license":"http://creativecommons.org/licenses/publicdomain/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Rama Rawat, R. K. Srivastava","submitted_at":"2009-08-17T14:15:46Z","abstract_excerpt":"Let $Z_{r,R}$ be the class of all continuous functions $f$ on the annulus $\\Ann(r,R)$ in the real hyperbolic space $\\mathbb B^n$ with spherical means $M_sf(x)=0$, whenever $s>0$ and $x\\in \\mathbb B^n$ are such that the sphere $S_s(x)\\subset \\Ann(r, R) $ and $B_r(o)\\subseteq B_s(x).$ In this article, we give a characterization for functions in $Z_{r,R}$. In the case $R=\\infty$, this result gives a new proof of Helgason's support theorem for spherical means in the real hyperbolic spaces."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0908.2289","kind":"arxiv","version":5},"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"}