{"paper":{"title":"Frame completions with prescribed norms: local minimizers and applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Demetrio Stojanoff, Noelia B. Rios, Pedro G. Massey","submitted_at":"2016-10-07T19:10:22Z","abstract_excerpt":"Let $\\mathcal F_0=\\{f_i\\}_{i\\in\\mathbb{I}_{n_0}}$ be a finite sequence of vectors in $\\mathbb C^d$ and let $\\mathbf{a}=(a_i)_{i\\in\\mathbb{I}_k}$ be a finite sequence of positive numbers. We consider the completions of $\\cal F_0$ of the form $\\cal F=(\\cal F_0,\\cal G)$ obtained by appending a sequence $\\cal G=\\{g_i\\}_{i\\in\\mathbb{I}_k}$ of vectors in $\\mathbb C^d$ such that $\\|g_i\\|^2=a_i$ for $i\\in\\mathbb{I}_k$, and endow the set of completions with the metric $d(\\cal F,\\tilde {\\mathcal F}) =\\max\\{ \\,\\|g_i-\\tilde g_i\\|: \\ i\\in\\mathbb{I}_k\\}$ where $\\tilde {\\cal F}=(\\cal F_0,\\,\\tilde {\\cal G})$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.02378","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"}