{"paper":{"title":"Stability estimates with a priori bound for the inverse local Radon transform","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Jan Boman, Joel Andersson","submitted_at":"2014-05-15T17:59:57Z","abstract_excerpt":"We consider the inverse problem for the $2$-dimensional weighted local Radon transform $R_m[f]$, where $f$ is supported in $y\\geq x^2$ and $R_m[f](\\xi,\\eta)=\\int f(x, \\xi x + \\eta) m(\\xi, \\eta, x)\\,\\text{d} x$ is defined near $(\\xi,\\eta)=(0,0)$. For weight functions satisfying a certain differential equation we give weak estimates of $f$ in terms of $R_m[f]$ for functions $f$ that satisfies an a priori bound."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1405.3922","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"}