7 problems

For $\Lambda\subset\mathbb N\cup\{0\}$ and a function $f$ holomorphic in a domain $D$ containing $0$, define $\langle f,D\rangle\in P_\Lambda$ if $f$ has a power-series expansion ……

Let $F$ be an infinite sequence of $p$-tuples of holomorphic functions $f=(f_1,\ldots,f_p)$ in the unit disc, with each $f_j$ having no zeros and satisfying … Assume the conclusion…

Let $F$ be an infinite sequence of $p$-tuples $f=(f_1,\ldots,f_p)$ of holomorphic functions in the unit disc, with each $f_j$ having no zeros and satisfying … For a subset…

Let $n\geq 2$, and let $f:\mathbb{R}^n\to\mathbb{R}^n$ be an entire quasiregular Yosida mapping, meaning that the family of translates … is normal. Order conjecture. The order of g…

Let $D$ be a domain and let $\mathcal{F}$ be a family of analytic functions on $D$ satisfying, for every $f\in\mathcal{F}$ and every $z\in D$, $f(z)\neq 0$ and $f'(z)\neq 1$. Monte…

Let $Z$ be a subset of $B_1\subset\mathbb{R}^n$, and let $F_Z$ be the set of harmonic functions $u$ in $B_1$ such that $Z(u)=Z$ and $u(0)=1$. Compactness conjecture for harmonic fu…

Let $D\subset\mathbb C$ be a domain, let $n\geq 2$, and let $\varepsilon>0$. Let $\mathcal F$ be the family of all holomorphic functions $f:D\to\mathbb C$ such that … for every fix…