{"paper":{"title":"Universal optimal configurations for the $p$-frame potentials","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA","math.IT"],"primary_cat":"cs.IT","authors_text":"Eric Goodman, Kasso Okoudjou, Shujie Kang, Victor Gonzales, Xuemei Chen","submitted_at":"2019-02-09T22:16:10Z","abstract_excerpt":"Given $d, N\\geq 2$ and $p\\in (0, \\infty]$ we consider a family of functionals, the $p$-frame potentials FP$_{p, N, d}$, defined on the set of all collections of $N$ unit-norm vectors in $\\mathbb R^d$. For the special case $p=2$ and $p=\\infty$, both the minima and the minimizers of these potentials have been thoroughly investigated. In this paper, we investigate the minimizers of the functionals FP$_{p, N, d}$, by first establishing some general properties of their minima. Thereafter, we focus on the special case $d=2$, for which, surprisingly, not much is known. One of our main results establi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1902.03505","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"}