{"paper":{"title":"The Spherical Mean Transform with Data on a Parabola in the Plane","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yehonatan Salman","submitted_at":"2018-01-29T14:06:19Z","abstract_excerpt":"In this paper we deal with the problem of recovering functions from their spherical mean transform $\\mathcal{R}$, which integrates functions on circles in the plane, in case where the centers of the circles of integration are located on a parabola $\\mathcal{P}$ while their radii can be chosen arbitrarily. Using our data, on the values of $\\mathcal{R}$ on $\\mathcal{P}$, we show how to extract its values in the exterior of $\\mathcal{P}$ in case where the functions in question have compact support inside $\\mathcal{P}$. Hence, one can use known inversion formulas for $\\mathcal{R}$ in the exterior "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.09512","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"}