We describe certain -algebras generated by Toeplitz operators with nilpotent symbols and acting on a poly-Bergman type space of the Siegel domain . Bounded measurable functions of the form are called nilpotent symbols. In this work, we consider symbols of the form , where both limits and exist, and belongs to the set of piecewise continuous functions on and having one-side limit values at each point of a finite set . We prove that the -algebra generated by all Toeplitz operators is isomorphic to , where and .

中文翻译：

---

二维Siegel域的True-Poly-Bergman类型空间上的Toeplitz算符：幂等符号

我们描述由Toeplitz算符生成的具有幂等符号的某些-代数，并作用于Siegel域的poly-Bergman类型空间。形式的可测函数被称为幂等符号。在这项工作中，我们考虑以下形式的符号，其中都存在极限并存在，并且属于上的分段连续函数集 并在有限集的每个点上都有一个极限值 。我们证明了-所有Toeplitz算子代数产生是同构的，在那里 和 。