Hankel向量矩序列与二元Pick函数无穷远点的非切正则性
Hankel vector moment sequences and the non-tangential regularity at infinity of two variable Pick functions
摘要：
$d$变量的Pick函数是从$Π^d$到$Π$的全纯映射，其中$Π$是上半平面。某些单变量的Pick函数在无穷远处有渐近展开式，一个幂级数$\sum_{n=1}^\infty ρ_n z^{-n}$与实数$ρ_n$，给出了一个渐近展开的非切向接近区域到无穷远处。H. Hamburger在1921年描述了哪些序列可以发生$\{ρ_n\} $。本文将Hamburger的结果推广到二元Pick函数.
英文摘要：
A Pick function of $d$ variables is a holomorphic map from $Π^d$ to $Π$, where $Π$ is the upper halfplane. Some Pick functions of one variable have an asymptotic expansion at infinity, a power series $\sum_{n=1}^\infty ρ_n z^{-n}$ with real numbers $ρ_n$ that gives an asymptotic expansion on non-tangential approach regions to infinity. H. Hamburger in 1921 characterized which sequences $\{ρ_n\} $ can occur. We give an extension of Hamburger's results to Pick functions of two variables.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
