论文标题
完整的Fock空间中的非交通合理功能
Non-commutative rational functions in the full Fock space
论文作者
论文摘要
当且仅当它在复杂的单元磁盘中限制时，有理功能属于Square-ummable Power系列的Hardy空间，即$ H^2 $。任何这样的理性函数都必须在大于一个半径的磁盘中分析。 $ \ mathfrak {r} \在h^2 $中的内部分解是特别简单的：$ \ mathfrak {r} $的内部因素是（有限的）blaschke产品，并且（因此）内部和外部因素再次是合理的。 我们将这些和其他基本事实扩展到$ h^2 $中的理性功能上，以$ \ mathbb {c}^d $上的完整fock空间在几个NC变量中标识为Square-ummable Power系列的\ emph {non-emph {non-emph {ncomph {nc hardy Space}。特别是，我们表征了何时NC合理函数属于Fock空间，我们证明了NC合理函数和NC多项式函数内部因素化的经典结果的类似物，并且我们获得了NC合理乘数的光谱结果。
A rational function belongs to the Hardy space, $H^2$, of square-summable power series if and only if it is bounded in the complex unit disk. Any such rational function is necessarily analytic in a disk of radius greater than one. The inner-outer factorization of a rational function, $\mathfrak{r} \in H^2$ is particularly simple: The inner factor of $\mathfrak{r}$ is a (finite) Blaschke product and (hence) both the inner and outer factors are again rational. We extend these and other basic facts on rational functions in $H^2$ to the full Fock space over $\mathbb{C}^d$, identified as the \emph{non-commutative (NC) Hardy space} of square-summable power series in several NC variables. In particular, we characterize when an NC rational function belongs to the Fock space, we prove analogues of classical results for inner-outer factorizations of NC rational functions and NC polynomials, and we obtain spectral results for NC rational multipliers.
