论文标题
自由非交通函数的蓝施克 - 单一阵容分解
Blaschke-Singular-Outer factorization of free non-commutative functions
论文作者
论文摘要
通过Herglotz和F. riesz的经典结果，复杂单元磁盘中的任何有限的分析功能都具有独特的内部分解。在这里，如果通过此函数乘法乘以乘以乘积，则称为\ emph {inner}或\ emph {outer}，分别定义了一个线性算子，或具有密集的范围，作为耐硬空间上的线性运算符，$ h^2 $，具有带有正方形的taylor taylor系列的复杂单元中的分析函数。可以进一步完善这种分解；任何内部函数$θ$均以独特的形式分解为\ emph {blaschke inner}函数和\ emph {单数内}函数的乘积，其中blaschke inner包含$θ$的所有消失信息，并且单数内部因子在单位磁盘中没有零。 我们证明了在完整的Fock空间的上下文中的这种分解的确切类似物，该分析功能的分析函数被确定为\ emph {非交换性hardy空间}，该函数在某些多变量的非交通式开放单元磁盘中定义了。
By classical results of Herglotz and F. Riesz, any bounded analytic function in the complex unit disk has a unique inner-outer factorization. Here, a bounded analytic function is called \emph{inner} or \emph{outer} if multiplication by this function defines an isometry or has dense range, respectively, as a linear operator on the Hardy Space, $H^2$, of analytic functions in the complex unit disk with square-summable Taylor series. This factorization can be further refined; any inner function $θ$ decomposes uniquely as the product of a \emph{Blaschke inner} function and a \emph{singular inner} function, where the Blaschke inner contains all the vanishing information of $θ$, and the singular inner factor has no zeroes in the unit disk. We prove an exact analog of this factorization in the context of the full Fock space, identified as the \emph{Non-commutative Hardy Space} of analytic functions defined in a certain multi-variable non-commutative open unit disk.
