论文标题
在poly-Disc上，Cowen-Douglas班上的一个同质运营商家族
A Family of Homogeneous Operators In The Cowen-Douglas Class Over The Poly-disc
论文作者
论文摘要
我们构建了一个众多的积极定义仁$ k：\ mathbb {d}^n \ times \ mathbb {d}^n \ to \ mbox {mbox {mbox {m}（r，\ mathbb c）$，在第二个变量和抗旋律中，与Quasi-Invariant相关，是Quasi-Invariant的， $\mbox{Möb} \times\cdots\times \mbox{Möb}$ ($n$ times) of the bi-holomorphic automorphism group of $\mathbb{D}^n$. $ n $ - 乘法运算符的乘以由$ k $确定的hilbert Space $ \ MATHCAL H_K $上的乘法运算符的乘积是同质的。我们表明，这些$ n $ - 元组是不可约的，在Cowen -Douglas类$ \ Mathrm b_r（\ Mathbb d^n）$中，并且它们是相互成对的单位不相等的。
We construct a large family of positive-definite kernels $K: \mathbb{D}^n\times \mathbb{D}^n \to \mbox{M} (r, \mathbb C)$, holomorphic in the first variable and anti-holomorphic in the second, that are quasi-invariant with respect to the subgroup $\mbox{Möb} \times\cdots\times \mbox{Möb}$ ($n$ times) of the bi-holomorphic automorphism group of $\mathbb{D}^n$. The adjoint of the $n$ - tuples of multiplication operators by the co-ordinate functions on the Hilbert spaces $\mathcal H_K$ determined by $K$ is then homogeneous with respect to this subgroup. We show that these $n$ - tuples are irreducible, are in the Cowen-Douglas class $\mathrm B_r(\mathbb D^n)$ and that they are mutually pairwise unitarily inequivalent.
