{"paper":{"title":"A breakdown of injectivity for weighted ray transforms in multidimensions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CA"],"primary_cat":"math.FA","authors_text":"Fedor Goncharov (CMAP), Roman Novikov (CMAP)","submitted_at":"2017-11-15T12:40:29Z","abstract_excerpt":"We consider weighted ray-transforms $P\\_W$ (weighted Radon transforms along straight lines) in $\\mathbb{R}^d, \\, d\\geq 2,$ with strictly positive weights $W$. We construct an example of such a transform with non-trivial kernel in the space of infinitely smooth compactly supported functions on $\\mathbb{R}^d$. In addition, the constructed weight $W$ is rotation-invariant continuous and is infinitely smooth almost everywhere on $\\mathbb{R}^d \\times \\mathbb{S}^{d-1}$. In particular, by this construction we give counterexamples to some well-known injectivity results for weighted ray transforms for "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.06163","kind":"arxiv","version":4},"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"}