{"paper":{"title":"Recovering stable kernels from exterior measurements","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Yi-Hsuan Lin","submitted_at":"2026-06-04T17:30:59Z","abstract_excerpt":"We study an inverse problem for translation-invariant symmetric stable operators of the form\n  \\begin{equation*}\n  L_a u(x)=\\mathrm{P.V.}\\int_{\\mathbb R^n}(u(x)-u(y))\\frac{a((x-y)/|x-y|)}{|x-y|^{n+2s}}\\,dy,\n  \\quad 0<s<1,\n  \\end{equation*}\n  where the unknown is the even angular density $a$ on $\\mathbb Sn$. For a bounded open set $\\Omega\\subset\\mathbb R^n$, with $\\Omega_e=\\mathbb R^n\\setminus\\overline\\Omega$, we consider restricted exterior Dirichlet-to-Neumann maps $\\Lambda_a^{W_1,W_2}$, where exterior data are supported in $W_1\\Subset\\Omega_e$ and the nonlocal Neumann data are observed on $W"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2606.06427","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2606.06427/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}