论文标题
频谱集，极端功能和特殊矩阵
Spectral sets, extremal functions and exceptional matrices
论文作者
论文摘要
令$ a $为正方形矩阵，让$ω$为$ a $的光谱中的飞机中的开放式套装。我们考虑了将操作员规范$ \ | f（a）\ | $最大化的问题中的所有holomorphic函数中的$ f $从$ω$中的所有holomorphic函数$ f $ in the封闭的单位磁盘中。如果$ f_0 $对于此问题是极端的，并且如果$ \ | | f_0（a）\ |> 1 $，那么事实证明，矩阵$ f_0（a）$具有特殊的属性，其中其主要的左和右奇异向量是相互正交的。我们研究此类杰出矩阵$ f_0（a）$。特别是，我们对上述正交性属性的特征程度感兴趣。
Let $A$ be a square matrix and let $Ω$ be an open set in the plane containing the spectrum of $A$. We consider the problem of maximizing the operator norm $\|f(A)\|$ amongst all holomorphic functions $f$ from $Ω$ into the closed unit disk. If $f_0$ is extremal for this problem and if $\|f_0(A)\|>1$, then it turns out that the matrix $f_0(A)$ has special properties, among them the fact that its principal left and right singular vectors are mutually orthogonal. We study this class of exceptional matrices $f_0(A)$. In particular, we are interested in the extent to which they are characterized by the aforementioned orthogonality property.
