{"paper":{"title":"Recovering Functions from the Spherical Mean Transform with Data on an Ellipse Using Eigenfunction Expansion in Elliptical Coordinates","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yehonatan Salman","submitted_at":"2017-05-16T12:36:05Z","abstract_excerpt":"The aim of this paper is to introduce a new inversion procedure for re- covering functions, defined on $\\Bbb R^{2}$, from the spherical mean transform, which integrates functions on a prescribed family $\\Lambda$ of circles, where $\\Lambda$ consists of circles whose centers belong to a given ellipse E on the plane. The method presented here follows the same procedure which was used by S. J. Norton in [22] for recovering functions in case where $\\Lambda$ consists of circles with centers on a circle. However, at some point we will have to modify the method in [22] by using expansion in elliptical"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05679","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"}