论文标题
带有有理矩阵的toeplitz式操作员
A Toeplitz-like operator with rational matrix symbol having poles on the unit circle: Fredholm properties
论文作者
论文摘要
本文涉及对有理矩阵函数产生的无界Toeplitz的算子的分析。它在[11,12,13]中遇到的t杆上具有标量合理函数产生的量表合理函数生成的该运算符的分析。证明了带有极点和零的零矩阵函数的Wiener-HOPF类型分解，然后被证明，然后用来分析这种类似Toeplitz的运算符的Fredholm性质。给出了基于分解的索引公式。此外，与经典案例相反，矩阵函数的决定因素不足以使toeplitz样算子成为弗雷德霍尔姆（Fredholm）。
This paper concerns the analysis of an unbounded Toeplitz-like operator generated by a rational matrix function having poles on the unit circle T. It extends the analysis of such operators generated by scalar rational functions with poles on T found in [11,12,13]. A Wiener-Hopf type factorization of rational matrix functions with poles and zeroes on T is proved and then used to analyze the Fredholm properties of such Toeplitz-like operators. A formula for the index, based on the factorization, is given. Furthermore, it is shown that the determinant of the matrix function having no zeroes on T is not sufficient for the Toeplitz-like operator to be Fredholm, in contrast to the classical case.
