10 problems

Let $(\mu_n)$ be a $\theta$-log-convex Stieltjes moment sequence, and let $(\mu_n^{\circ t})$ denote its Maxwell-Boltzmann convolution semigroup for $t\in\mathbf{R}_+$. The precedi…

Let $\mu$ be a finitely atomic Berger measure with support in $\mathbb{R}_+$. Curto's conjecture. The following statements are equivalent. This conjecture concerns the relationship…

Let $W_\mu$ be a recursively generated (i.e., $\operatorname{card}\operatorname{supp}\mu<\infty$) subnormal weighted shift. Curto's conjecture. The following statements are equival…

Let $\psi_{n,k}$ be the number of functional digraphs on $[n]$ with $k$ cyclic vertices, let $\Psi_n(y)=\sum_{k=0}^n\psi_{n,k}y^k$, and let $\Psi=(\psi_{n,k})_{n,k\geq 0}$. A matri…

Let $a,b\in \mathbb{R}$ with $0<a<b$. Let $(n_k)_{k \in \mathbb{N}}$ be a strictly increasing sequence of positive integers such that … A non-trivial signed measure with prescribed…

A sequence of positive integers is called a Müntz–Szász sequence when the reciprocal series of its terms diverges. Replication conjecture. For any sequence which is not a Müntz–Szá…

Let $r$ be the number of parameters, let ${\mathbf{k}}\in {\mathbb N}^r$ be a multi-index, let $x$ be an indeterminate, and let ${\bm{\beta}}=(\beta_1,\ldots,\beta_r)$ be a vector…

Alternating Turán-type inequality. For all $n\geq 0$ and $j,k\geq 1$, one has

Alternating moment identity.

Conjectural derivative identity.