Inversion of the Toeplitz-block Toeplitz matrices and the structure of the corresponding inverse matrices
Classical Analysis and ODEs
2020-07-03 v1 Functional Analysis
Rings and Algebras
Abstract
The results on the inversion of convolution operators and Toeplitz matrices in the 1-D (one dimensional) case are classical and have numerous applications. We consider a 2-D case of Toeplitz-block Toeplitz matrices, describe a minimal information, which is necessary to recover the inverse matrices, and give a complete characterisation of the inverse matrices.
Keywords
Cite
@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}
}
Comments
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