Let $\mathbb{H}=\{z\in\mathbb{C}:\operatorname{Im}z>0\}$, and let $N(\mathbb{H})$ denote the Nevanlinna class in $\mathbb{H}$, consisting of meromorphic functions representable as quotients of two bounded analytic functions in $\mathbb{H}$. We construct a nonconstant meromorphic function $F$ on $\mathbb{C}$ such that $...
In 1928 H. Cartan stated a conjecture about holomorphic curves in $\mathbb{P}^n$ parametrized by the unit disc, omitting $n+2$ hyperplanes in general position. He proved it for $n=2$. In 1996 the first-named author constructed counterexamples for all $n\geq 3$, and proposed a modified form of Cartan's conjecture which...
Let $\mathcal{M}$ be a von Neumann algebra equipped with a faithful normal semifinite weight, and let $L_p(\mathcal{M})$ denote the associated Haagerup noncommutative $L_p$-space. For $1<p<\infty$, let $q=p/(p-1)$. For $z\in L_q(\mathcal{M})$ and $y\in L_p(\mathcal{M})$, denote by $\langle z,y\rangle=\operatorname{Re}\...
Zong-Ben Xu, Teng-Ren Zhang· 0 citations
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