Fock空间上的Schur类乘子：de Branges-Rovnyak再生核空间和传递函数实现
Schur-class multipliers on the Fock space: de Branges-Rovnyak reproducing kernel spaces and transfer-function realizations
摘要：
本文引入并研究了de Branges-Rovnyak型再生核希尔伯特空间的Fock空间非交换模拟。成果包括：使用de Branges-Rovnyak空间${\mathcal H}(K_{S})$作为Schur类乘法器$S$的唯一（直到酉等价）可观测的、共轴传递函数实现的状态空间，内部Schur类乘法器的实现理论表征，以及用于获得具有规定的左零结构的内部乘法器的实现的演算。与单位球${\mathbb B}^{d} \subset {\mathbb C}^{d}$上的Arveson空间的平行理论（可以看作这里使用的Fock空间的对称化版本）相比，这里的结果更符合经典的单变量情况，所有结果的存在性的额外成分都有"左“和"右”版本。
英文摘要：
We introduce and study a Fock-space noncommutative analogue of reproducing kernel Hilbert spaces of de Branges-Rovnyak type. Results include: use of the de Branges-Rovnyak space ${\mathcal H}(K_{S})$ as the state space for the unique (up to unitary equivalence) observable, coisometric transfer-function realization of the Schur-class multiplier $S$, realization-theoretic characterization of inner Schur-class multipliers, and a calculus for obtaining a realization for an inner multiplier with prescribed left zero-structure. In contrast with the parallel theory for the Arveson space on the unit ball ${\mathbb B}^{d} \subset {\mathbb C}^{d}$ (which can be viewed as the symmetrized version of the Fock space used here), the results here are much more in line with the classical univariate case, with the extra ingredient of the existence of all results having both a ``left'' and a ``right'' version.
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