{"paper":{"title":"On (conditional) positive semidefiniteness in a matrix-valued context","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Fritz Gesztesy, Michael Pang","submitted_at":"2016-02-01T03:53:03Z","abstract_excerpt":"In a nutshell, we intend to extend Schoenberg's classical theorem connecting conditionally positive semidefinite functions $F\\colon \\mathbb{R}^n \\to \\mathbb{C}$, $n \\in \\mathbb{N}$, and their positive semidefinite exponentials $\\exp(tF)$, $t > 0$, to the case of matrix-valued functions $F \\colon \\mathbb{R}^n \\to \\mathbb{C}^{m \\times m}$, $m \\in \\mathbb{N}$. Moreover, we study the closely associated property that $\\exp(t F(- i \\nabla))$, $t>0$, is positivity preserving and its failure to extend directly in the matrix-valued context."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.00384","kind":"arxiv","version":3},"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"}