We generalize the notion of bounded point evaluation introduced by Williams for a cyclic operator to a finitely multicyclic commuting d-tuple $T=(T_1,\dots ,T_d)$ of bounded linear operators on a complex separable Hilbert space. We show that the set $bpe(T)$ of all bounded point evaluations for T is a unitary invariant and we characterize it in terms of the dimension of the joint cokernel of T. Using this, we show that if $bpe(T)$ has non-empty interior, then T can be realized as the d-tuple ${\mathcal{M}}_z=({\mathcal{M}}_{z_1},\dots ,{\mathcal{M}}_{z_d})$ of multiplication operators on a reproducing kernel Hilbert space $\mathcal{H}$ of functions on $bpe(T)$. We further characterize the largest open subset of $bpe(T)$ on which all the elements of $\mathcal{H}$ are analytic, which we refer to as the set of all analytic bounded point evaluations. As an application, we describe the set of all analytic bounded point evaluations for toral and spherical isometries, and also, derive an analytic model of a commuting d-tuple of composition operators.

我们将威廉姆斯针对循环算子引入的有界点评估概念推广到有限多循环通勤d-元组$Ť=（{Ť}_{\mathrm{1个}}，\dots ，{Ť}_d）$复杂可分离Hilbert空间上的有界线性算子 我们展示了$bpË（Ť）$T的所有边界点估计中的一个是一个不变式，我们用T的联合核的维数来表征它。使用这个，我们表明$bpË（Ť）$具有非空内部，则T可实现为d-元组${\mathcal{中号}}_{ž}=（{\mathcal{中号}}_{{ž}_{\mathrm{1个}}}，\dots ，{\mathcal{中号}}_{{ž}_d}）$ 再生内核希尔伯特空间上乘法运算符的映射 $\mathcal{H}$ 的功能 $bpË（Ť）$。我们进一步表征最大的开放子集$bpË（Ť）$ 在其中的所有元素 $\mathcal{H}$是解析的，我们称为所有解析边界点评估的集合。作为一种应用，我们描述了对圆和球面等距的所有解析界点评估的集合，并且还推导了合成算子的d个元组的通勤解析模型。