Toeplitz块Toeplitz矩阵的求逆及相应逆矩阵的结构
经典分析与常微分方程
2020-07-03 v1 泛函分析
环与代数
摘要
一维（one dimensional）情形下卷积算子和Toeplitz矩阵求逆的结果是经典的，并有大量应用。我们考虑Toeplitz块Toeplitz矩阵的二维情形，描述了恢复逆矩阵所需的最小信息，并给出了逆矩阵的完整刻画。
引用
@article{arxiv.1704.02267,
title = {Inversion of the Toeplitz-block Toeplitz matrices and the structure of the corresponding inverse matrices},
author = {Alexander Sakhnovich},
journal= {arXiv preprint arXiv:1704.02267},
year = {2020}
}
备注
The ideas and proofs given in this paper are easily modified for the case of convolution operators (see some results on the inversion of the 2-D convolution operators in arXiv:1701.08559, where we mostly omit the proofs). However, the results obtained for the Toeplitz-block Toeplitz matrices are more complete