论文标题
完整的规范保留全体形态功能的扩展
Complete Norm Preserving Extensions of Holomorphic Functions
论文作者
论文摘要
我们表明，对于每个连接的分析子各种$ v $，都有一个pseudoconvex set $ω$，使得$ v $上的每个有界矩阵值的全体形态函数在$ v $上延伸至$ω$。我们证明，如果$ v $是两个分析磁盘在一个点相交的两个分析磁盘，如果每个有界的标量均值全体形态函数均等地扩展到$ω$，那么每个矩阵值值功能也是如此。在特殊情况下，$ω$是对称的bidisk，我们表明这不能通过从一个点消失的函数中找到线性等距扩展来完成。
We show that for every connected analytic subvariety $V$ there is a pseudoconvex set $Ω$ such that every bounded matrix-valued holomorphic function on $V$ extends isometrically to $Ω$. We prove that if $V$ is two analytic disks intersecting at one point, if every bounded scalar valued holomorphic function extends isometrically to $Ω$, then so does every matrix-valued function. In the special case that $Ω$ is the symmetrized bidisk, we show that this cannot be done by finding a linear isometric extension from the functions that vanish at one point.
