6 problems

Laplace-transform criterion. The function $L_m$ is the Laplace transform of some random variable if and only if $m=0$, corresponding to a trivial random variable, or $m\ge e$.

Finite Laplace transform question. Can the finite Laplace transform of this function be expressed in terms of the Fox H-function?

Let $\mathcal{P}_{\bm{t}}$ and $\bm{V}_s$ be as in Proposition. For a coordinate $k$, define the moment … Let $\Delta$, $\boldsymbol{\lambda}$, and the inverse Laplace operators…

Polynomial-form conjecture. This integral is of the form

Let $A$ and $B$ be Hermitian $n\times n$ matrices, with $B$ positive semidefinite. Let $\operatorname{Tr}$ denote the trace. Bessis–Moussa–Villani conjecture. The function … is the…

Let ${\mathcal M}$ be the subspace of polynomials $f(\xi,z)\in{\mathbb C}[\xi,z]$ such that ${\mathcal Z}(f)$ has no holomorphic part, equivalently such that the Laplace transforma…