论文标题
克拉克措施和多个变量中的De Branges-Rovnyak空间
Clark measures and de Branges-Rovnyak spaces in several variables
论文作者
论文摘要
令$ b_n $表示$ \ mathbb {c}^n $，$ n \ ge 1 $的单位球，然后$ b_ {n_j} $，$ j \ ge 1 $。给定一个非恒定全体形态函数$ b：\ MATHCAL {d} \至B_1 $，我们研究了Clark的clark the Clark the Clark的相应家族$σ_α[b] $，$α\ in \ in \ in \ in \ in \ in \ int \ int \ in \ int \ portial b_1 $，在杰出的边界$ \ partial $ \ partial \ mathcal {d d} $上测量。我们从de Branges-Rovnyak空间$ \ Mathcal {h}（b）$构建一个天然的统一运算符上$ h^2（σ_α）$。作为一个应用程序，对于$ \ Mathcal {d} = b_n $和一个内部函数$ i：b_n \ to b_1 $，我们表明属性$σ_1[i] \llσ_1[b] $与$ \ nathcal {h}（b）$中适当的显式函数的成员直接相关。
Let $B_n$ denote the unit ball of $\mathbb{C}^n$, $n\ge 1$, and let $\mathcal{D}$ denote a finite product of $B_{n_j}$, $j\ge 1$. Given a non-constant holomorphic function $b: \mathcal{D} \to B_1$, we study the corresponding family $σ_α[b]$, $α\in\partial B_1$, of Clark measures on the distinguished boundary $\partial\mathcal{D}$. We construct a natural unitary operator from the de Branges-Rovnyak space $\mathcal{H}(b)$ onto the Hardy space $H^2(σ_α)$. As an application, for $\mathcal{D}= B_n$ and an inner function $I: B_n \to B_1$, we show that the property $σ_1[I]\llσ_1[b]$ is directly related to the membership of an appropriate explicit function in $\mathcal{H}(b)$.
