{"paper":{"title":"On the Determination of a Function from an Elliptical Radon Transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Sunghwan Moon","submitted_at":"2013-02-18T19:34:20Z","abstract_excerpt":"In recent years, Radon type transforms that integrate functions over various sets of ellipses/ellipsoids have been considered in SAR, ultrasound reflection tomography, and radio tomography. In this paper, we consider the transform that integrates a given function in $\\RR^n$ over a set of solid ellipsoids of rotation with a fixed eccentricity and foci restricted to a hyperplane. Inversion formulas are obtained for appropriate classes of functions that are even with respect to the hyperplane. Stability estimates, range description, and local uniqueness results are also provided."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.4396","kind":"arxiv","version":6},"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"}