11 problems

Let $K$ be the compact Lie group considered in the paper, let $K_{\mathbb C}$ be its complexification, let $t>0$, and let $C_t$ denote the generalized Segal–Bargmann transform from…

Let $R$ be a simply connected convex region of a discrete Riemann surface, and let the associated discrete exponentials be holomorphic functions on $R$. Exponential-generation conj…

Krzyż's conjecture. For every $f\in\Omega$ and every $n\geq 1$,

Let $\mathbb{D}$ be the unit disk, and let $\operatorname{Cara}(\mathbb{D};2,3)$ be the set of ×2- and ×3-circular Carathéodory functions; call an element rational extreme when it…

Let $\mathbb{D}$ be the unit disk, and let $\operatorname{Cara}(\mathbb{D};2,3)$ be the set of Carathéodory functions that are ×2- and ×3-circular, where ×$n$-circular means…

Let $\mathbb{D}$ be the unit disk, and let $\operatorname{Cara}(\mathbb{D};2,3)$ be the set of holomorphic functions $\psi:\mathbb{D}\to\mathbb{C}$ with…

Let $\Omega$ be a domain, let $B(\Omega)$ be a Banach space of holomorphic functions on $\Omega$, and let $\mathcal{M}(B(\Omega))$ denote its algebra of multipliers. Multiplier rec…

Let $\Omega$ be a domain and let $B(\Omega)$ be the Banach space of holomorphic functions on $\Omega$. Reciprocal conjecture. If $\psi\in B(\Omega)$ and there exists a constant…

Let $\mathbb{B}_n$ denote the unit ball, and let $A^p_\alpha$ be the weighted Bergman space on $\mathbb{B}_n$, where $0<p<\infty$ and $\alpha$ is real. Zhu's reciprocal conjecture.…

Let $\mathcal{A}$ be a family of complex holomorphic functions. Let $z\in\mathbb{C}^{n}$, let $U$ be an open neighbourhood of $z$, and let $f:U\rightarrow\mathbb{C}$ be holomorphic…

Huang et al.'s conjecture. Under these assumptions, $f$ vanishes identically.