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The results on the inversion of convolution operators and Toeplitz matricesin 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 minimalinformation, which is necessary to recover the inverse matrices, and give acomplete characterisation of the inverse matrices.

Inversion of the Toeplitz-block Toeplitz matrices and the structure of the corresponding inverse matrices