论文标题
与常规多域相关的多对eplitz运算符
Multi-Toeplitz operators associated with regular polydomains
论文作者
论文摘要
在本文中，我们介绍并研究了与非共同多域相关的加权多toeplitz运算符$ {\ bf d_f^m} $，$ {\ bf m}：=（m_1，\ ldots，m_k）\ in {\ bf n}^k $ f}：=（f_1，\ ldots，f_k）$在原点附近的正常自由全体形态功能。这些操作员正在对张量产品$ f^2（h_ {n_1}）\ otimes \ cdots \ cdots \ otimes f^2（h_ {n_k}）$ a $ n_i $ n_i $生成器或同等地，它们可以被视为多型eplitz operators acts occopt ocy ockoct ockoct ockoct ockoct ockoct ockoct ockoct ockock fuffer flfloce forflock forflock forflock forte forted flfloce。对于大型的多域，我们表明没有非零紧凑的多toeplitz运算符。我们根据$ {\ bf d_f^m} $的径向函数有界的$ k $ -pluriharmonic函数来表征加权的多toeplitz运算符，并使用结果来获得dirichlet扩展问题的类似物，以获取$ k $ $ - $ -pluriharmaron的函数。我们表明，加权的多型ePlitz运算符具有非交通傅里叶表示形式，可以将其视为非交通符号，可用于恢复关联的操作员。我们还证明，加权的多用途运算符满足与polydomain $ {\ bf d_f^m} $相关的棕色-HALMOS类型方程。
In this paper we introduce and study the class of weighted multi-Toeplitz operators associated with noncommutative polydomains ${\bf D_f^m}$, ${\bf m}:=(m_1,\ldots, m_k)\in {\bf N}^k$, generated by $k$-tuples ${\bf f}:=(f_1,\ldots, f_k)$ of positive regular free holomorphic functions in a neighborhood of the origin. These operators are acting on the tensor product $F^2(H_{n_1})\otimes \cdots \otimes F^2(H_{n_k})$ of full Fock spaces with $n_i$ generators or, equivalently, they can be viewed as multi-Toeplitz operators acting on tensor products of weighted full Fock spaces. For a large class of polydomains, we show that there are no non-zero compact multi-Toeplitz operators. We characterize the weighted multi-Toeplitz operators in terms of bounded free $k$-pluriharmonic functions on the radial part of ${\bf D_f^m}$ and use the result to obtain an analogue of the Dirichlet extension problem for free $k$-pluriharmonic functions. We show that the weighted multi-Toeplitz operators have noncommutative Fourier representations which can be viewed as noncommutative symbols and can be used to recover the associated operators. We also prove that the weighted multi-Toeplitz operators satisfy a Brown-Halmos type equation associated with the polydomain ${\bf D_f^m}$.
