{"paper":{"title":"Geometry and Singularities of the Prony mapping","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Dmitry Batenkov, Yosef Yomdin","submitted_at":"2013-01-07T13:36:06Z","abstract_excerpt":"Prony mapping provides the global solution of the Prony system of equations \\[ \\Sigma_{i=1}^{n}A_{i}x_{i}^{k}=m_{k},\\ k=0,1,...,2n-1. \\] This system appears in numerous theoretical and applied problems arising in Signal Reconstruction. The simplest example is the problem of reconstruction of linear combination of $\\delta$-functions of the form $g(x)=\\sum_{i=1}^{n}a_{i}\\delta(x-x_{i})$, with the unknown parameters $a_{i},\\ x_{i},\\ i=1,...,n,$ from the \"moment measurements\" $m_{k}=\\int x^{k}g(x)dx.$\n  Global solution of the Prony system, i.e. inversion of the Prony mapping, encounters several ty"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.1336","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"}