{"paper":{"title":"Momentum ray transforms","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ramesh Manna, Suman Kumar Sahoo, Venkateswaran P. Krishnan, Vladimir Sharafutdinov","submitted_at":"2018-08-02T11:55:27Z","abstract_excerpt":"The momentum ray transform $I^k$ integrates a rank $m$ symmetric tensor field $f$ over lines with the weight $t^k$:\n  $\n  (I^k\\!f)(x,\\xi)=\\int_{-\\infty}^\\infty t^k\\langle f(x+t\\xi),\\xi^m\\rangle\\,dt.\n  $\n  In particular, the ray transform $I=I^0$ was studied by several authors since it had many tomographic applications. We present an algorithm for recovering $f$ from the data $(I^0\\!f,I^1\\!f,\\dots, I^m\\!f)$. In the cases of $m=1$ and $m=2$, we derive the Reshetnyak formula that expresses $\\|f\\|_{H^s_t({\\mathbb{R}}^n)}$ through some norm of $(I^0\\!f,I^1\\!f,\\dots, I^m\\!f)$. The $H^{s}_{t}$-norm i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1808.00768","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"}