论文标题
与非交通性多型球相关的多用量ePlitz运算符的棕色钟表表征
Brown-Halmos characterization of multi-Toeplitz operators associated with noncommutative poly-hyperballs
论文作者
论文摘要
我们获得了Louhichi的非交通性多变量类似物和Olofsson的表征，对Toeplitz操作员进行了谐波符号的特征，并在加权的Bergman Space $ a_m（{\ bf d}）上以及Eschmeier和Eschmeier and Langendorfer扩展到$ {\ bf c}^n $。 All our results are proved in the more general setting of noncommutative poly-hyperballs ${\bf D_n^m}(H)$, ${\bf n,m}\in {\bf N}^k$, and are used to characterize the bounded free $k$-pluriharmonic functions with operator coefficients on poly-hyperballs and to solve the associated Dirichlet extension problem.特别是，结果可用于繁殖内核空间 $$ κ_ {\ bf m}（z，w）：= \ prod_ {i = 1}^k \ frac {1} {（1- \ bar z_i w_i）^{m_i}}，\ qquad z，w \ in {\ bf d}^k，w \ $$ 其中$ m_i \ geq 1 $。这包括耐寒的空间，伯格曼空间以及多迪斯克上的加权伯格曼空间。
We obtain a noncommutative multivariable analogue of Louhichi and Olofsson characterization of Toeplitz operators with harmonic symbols on the weighted Bergman space $A_m({\bf D})$, as well as Eschmeier and Langendorfer extension to the unit ball of ${\bf C}^n$. All our results are proved in the more general setting of noncommutative poly-hyperballs ${\bf D_n^m}(H)$, ${\bf n,m}\in {\bf N}^k$, and are used to characterize the bounded free $k$-pluriharmonic functions with operator coefficients on poly-hyperballs and to solve the associated Dirichlet extension problem. In particular, the results hold for the reproducing kernel Hilbert space with kernel $$ κ_{\bf m}(z,w):=\prod_{i=1}^k \frac{1}{(1-\bar z_i w_i)^{m_i}},\qquad z,w\in {\bf D}^k, $$ where $m_i\geq 1$. This includes the Hardy space, the Bergman space, and the weighted Bergman space over the polydisk.
