5 problems

Let $f\in\mathbb C(z,w)$ and $f_\infty\in\mathscr H(\infty)$. Assume the setting of the subsection in which $E\subset\mathbb R$, $E\cap F=\varnothing$, and $F$ is symmetric with re…

Let $f\in\mathbb C(z,w)$, let $w_\infty$ be the specified element of the function $w$, and let $f_\infty\in\mathscr H(\infty)$ be the corresponding element of $f$. For each…

Let $f$ belong to the Laguerre class $\mathscr L$, represented by … where $\alpha_j\in\mathbb R\setminus\mathbb Z$, $e_j\in\mathbb R$, and $e_1<\dots<e_{2q}$. Assume that $1,f,f^2$…

Angelesco uniqueness conjecture. The measure $\mu=\lambda_1+\lambda_2$ is the only positive Borel measure in the plane satisfying these inequalities and $\mu(\mathbb C)=2$. This un…

Let ${\bf f}=(f_1,\ldots,f_d)$ and ${\bf m}=(m_1,\ldots,m_d)\in\mathbb{Z}_+^d\setminus\{{\bf 0}\}$, and suppose that the denominator $Q_{n,\bf m}$ is unique for all sufficiently la…