In this paper, we describe the matrix representations of asymmetric truncated Toeplitz operators acting between two finite-dimensional model spaces \(K_1\) and \(K_2\). The novelty of our approach is that here we consider matrix representations computed with respect to bases of different type in \(K_1\) and \(K_2\) (for example, kernel basis in \(K_1\) and conjugate kernel basis in \(K_2\)). We thus obtain new matrix characterizations which are simpler than the ones already known for asymmetric truncated Toeplitz operators.

中文翻译：

---

不对称截断Toeplitz算子的矩阵表示

在本文中，我们描述了在两个有限维模型空间\（K_1 \）和\（K_2 \）之间起作用的不对称截断Toeplitz算子的矩阵表示。我们方法的新颖之处在于，这里我们考虑针对\（K_1 \）和\（K_2 \）中不同类型的基数计算出的矩阵表示形式（例如，\（K_1 \）中的核基和\\ K中的共轭核基）。 （K_2 \））。因此，我们获得了比不对称截断的Toeplitz算子已知的矩阵特征更简单的新矩阵特征。