On the inversion of the block double-structured and of the triple-structured Toeplitz matrices and on the corresponding reflection coefficients
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
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2020
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| _version_ | 1866929299672530944 |
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| author | Roitberg, Inna Sakhnovich, Alexander |
| author_facet | Roitberg, Inna Sakhnovich, Alexander |
| contents | The results on the inversion of convolution operators as well as Toeplitz (and block Toeplitz) matrices in the $1$-D (one-dimensional) case are classical and have numerous applications. Last year, we considered the $2$-D case of Toeplitz-block Toeplitz (TBT) matrices, described a minimal information, which is necessary to recover the inverse matrices, and gave a complete characterisation of the inverse matrices. Now, we develop our approach for the more complicated cases of block TBT-matrices and $3$-D Toeplitz matrices. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2006_15867 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | On the inversion of the block double-structured and of the triple-structured Toeplitz matrices and on the corresponding reflection coefficients Roitberg, Inna Sakhnovich, Alexander Classical Analysis and ODEs Functional Analysis Rings and Algebras 15A09, 15B05, 94A99 The results on the inversion of convolution operators as well as Toeplitz (and block Toeplitz) matrices in the $1$-D (one-dimensional) case are classical and have numerous applications. Last year, we considered the $2$-D case of Toeplitz-block Toeplitz (TBT) matrices, described a minimal information, which is necessary to recover the inverse matrices, and gave a complete characterisation of the inverse matrices. Now, we develop our approach for the more complicated cases of block TBT-matrices and $3$-D Toeplitz matrices. |
| title | On the inversion of the block double-structured and of the triple-structured Toeplitz matrices and on the corresponding reflection coefficients |
| topic | Classical Analysis and ODEs Functional Analysis Rings and Algebras 15A09, 15B05, 94A99 |
| url | https://arxiv.org/abs/2006.15867 |