{"paper":{"title":"Minimal scalings and structural properties of scalable frames","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Alice Chan, Hong Suh, Rachel Domagalski, Sivaram K. Narayan, Xingyu Zhang, Yeon Hyang Kim","submitted_at":"2015-08-10T14:48:37Z","abstract_excerpt":"For a unit-norm frame $F = \\{f_i\\}_{i=1}^k$ in $\\R^n$, a scaling is a vector $c=(c(1),\\dots,c(k))\\in \\R_{\\geq 0}^k$ such that $\\{\\sqrt{c(i)}f_i\\}_{i =1}^k$ is a Parseval frame in $\\R^n$. If such a scaling exists, $F$ is said to be scalable. A scaling $c$ is a minimal scaling if $\\{f_i : c(i)>0\\}$ has no proper scalable subframe. It is known that the set of all scalings of $F$ is a convex polytope whose vertices correspond to minimal scalings. In this paper, we provide an estimation of the number of minimal scalings of a scalable frame and a characterization of when minimal scalings are affinel"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02266","kind":"arxiv","version":2},"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"}