8 problems

For each $n\in\mathbb{N}$, let $X_n^\star$ be the idealizer associated with quasi-stable polynomials, and let $Y_n^\star$ be the corresponding family defined by $Y_n^\star=Y_n$ for…

For each $n\in\mathbb{N}$, let $X_n\subset\mathbb{R}_n^+$ be the largest subsemigroup containing $\mathcal{H}_n$ and $\mathbb{I}_n$ such that, for every $m\leq n$, Hadamard multipl…

Let $\{\gamma_i\}_{i\geq 0}$ be a shifted multiplier sequence that is eventually increasing, and define … The Turán-transform preservation conjecture. For every $j\in\mathbb{N}$, t…

Let $\{\gamma_i\}_{i\geq 0}$ be a shifted multiplier sequence that is eventually increasing. For $j\in\mathbb{N}$, let $T_j$ denote the order-$j$ Turán operator, and write…

Let $\{\gamma_i\}_{i\geq 0}$ be a multiplier sequence, and let $T_2$ denote the Turán operator, with … A sequence is infinitely-log-concave if $T_2^{(k)}(i)\geq 0$ for every…

Consider the sequence … A pair $(b,c)$ lies in the multiplier sequence region when this sequence is a multiplier sequence for the Legendre basis. Quartic Legendre multiplier sequen…

Square-root factorial series conjecture. The function $\varphi$ belongs to the Laguerre–Pólya class with nonnegative coefficients, denoted $\mathscr{L}-\mathscr{P}^{+}$.

Coefficient-formula conjecture. The coefficients satisfy