{"paper":{"title":"The matrix function $e^{tA+B}$ is representable as the Laplace transform of a matrix measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Victor Katsnelson","submitted_at":"2016-09-13T14:44:01Z","abstract_excerpt":"Given a pair $A,B$ of matrices of size $n\\times n$, we consider the matrix function $e^{At+B}$ of the variable $t\\in\\mathbb{C}$. If the matrix $A$ is Hermitian, the matrix function $e^{At+B}$ is representable as the bilateral Laplace transform of a matrix-valued measure $M(d\\lambda)$ compactly supported on the real axis: $$e^{At+B}=\\int{}e^{\\lambda t}\\,M(d\\lambda).$$\n  The values of the measure $M(d\\lambda)$ are matrices of size $n\\times n$, the support of this measure is contained in the convex hull of the spectrum of $A$. If the matrix $B$ is also Hermitian, then the values of the measure $M"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1609.03870","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"}