Further implications of the Bessis-Moussa-Villani conjecture (Q690625)

Bessis, Moussa and Villani conjectured that for hermitian matrices \(A\) and \(B\) with \(B\) positive, the function \(\operatorname{Trexp}(A-\lambda B)\) is the Laplace transform of a positive measure defined on the positive axis. This conjecture has been proven recently, and the purpose herein is to derive some new implications.