{"paper":{"title":"Krylov Subspace Methods in Dynamical Sampling","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.IT"],"primary_cat":"cs.IT","authors_text":"Akram Aldroubi, Ilya Krishtal","submitted_at":"2014-12-04T02:04:46Z","abstract_excerpt":"Let $B$ be an unknown linear evolution process on $\\mathbb C^d\\simeq l^2(\\mathbb Z_d)$ driving an unknown initial state $x$ and producing the states $\\{B^\\ell x, \\ell = 0,1,\\ldots\\}$ at different time levels. The problem under consideration in this paper is to find as much information as possible about $B$ and $x$ from the measurements $Y=\\{x(i)$, $Bx(i)$, $\\dots$, $B^{\\ell_i}x(i): i \\in \\Omega\\subset \\mathbb Z^d\\}$. If $B$ is a \"low-pass\" convolution operator, we show that we can recover both $B$ and $x$, almost surely, as long as we double the amount of temporal samples needed in \\cite{ADK13"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.1538","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"}