Scalar-type kernels for block Toeplitz operators
Scalar-type kernels for block Toeplitz operators
复制标题
用于块 Toeplitz 算子的标量型内核
DOI：
10.1016/j.jmaa.2020.124111
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发表时间：
2018
影响因子：
1.3
通讯作者：
J. Partington
中科院分区：
文献类型：
--
作者：
M. Cristina Câmara;J. Partington
结果表明，具有 2× 2 符号 G 的 Toeplitz 算子的核可以用非常宽的类中的任何给定函数、其与 G 相乘的图像以及它们的左逆（如果后者存在）来精确描述。因此，在许多情况下，块托普利茨算子的内核可以被描述为标量复值函数的空间与函数的固定列向量的乘积。这样的内核被称为标量类型，本文在许多具体情况下对它们进行了明确的研究和描述。给出了确定几个新类别符号的截断托普利茨算子核的应用。
It is shown that the kernel of a Toeplitz operator with 2× 2 symbol G can be described exactly in terms of any given function in a very wide class, its image under multiplication by G, and their left inverses, if the latter exist. As a consequence, under many circumstances the kernel of a block Toeplitz operator may be described as the product of a space of scalar complex-valued functions by a fixed column vector of functions. Such kernels are said to be of scalar type, and in this paper they are studied and described explicitly in many concrete situations. Applications are given to the determination of kernels of truncated Toeplitz operators for several new classes of symbols.