$\mathbb K$-齐次乘法算子在有界对称域上的次正规性
The Subnormality of $\mathbb K$-Homogeneous Multiplication Operators on Bounded Symmetric Domains
- Indian Institute of Technology Madras（印度马德拉斯理工学院）
机构由 AI 辅助整理，请以论文原文为准。
AI总结：
研究不可约有界对称域上由K-不变核决定的再生核Hilbert空间中坐标函数诱导的乘法算子的联合次正规性，引入压缩d元组概念，证明加权Bergman移位为压缩d元组当且仅当联合次正规，并通过扭曲矩问题与Hausdorff矩问题的等价性给出矩论刻画。
AI中文摘要：
设 $\Omega=G/\mathbb K$ 为秩 $r$、维数 $d$ 的不可约有界对称域。本文研究了由坐标函数在由 $\mathbb K$-不变核决定的 $\Omega$ 上全纯函数的再生核 Hilbert 空间上诱导的 $d$ 元乘法算子的联合次正规性。我们引入了与 $\Omega$ 相关联的压缩 $d$ 元组的概念，并证明了 $\Omega$ 上的加权 Bergman 移位恰好是压缩 $d$ 元组当且仅当它们是联合次正规的。联合次正规性的一个刻画进一步引出了一类矩问题的研究，我们称之为扭曲矩问题。我们建立了扭曲矩问题等价于一个适当的 Hausdorff 矩问题。这一等价性为所考虑的乘法算子的联合次正规性提供了矩论刻画。
英文摘要：
Let $Ω=G/\mathbb K$ be an irreducible bounded symmetric domain of rank $r$ and dimension $d.$ In this paper, we study the joint subnormality of $d$-tuple of multiplication operators induced by the coordinate functions on reproducing kernel Hilbert spaces of holomorphic functions on $Ω$ determined by $\mathbb K$-invariant kernels. We introduce the notion of contractive $d$-tuple associated with $Ω$ and prove that the weighted Bergman shifts on $Ω$ are contractive $d$-tuple precisely when they are jointly subnormal. A characterization of joint subnormality further leads to the study of a class of moment problems, which we refer to as twisted moment problems. We establish that the twisted moment problem is equivalent to an appropriate Hausdorff moment problem. This equivalence provides a moment-theoretic characterization of joint subnormality for the multiplication operators under consideration.
