Approximating Inverse of Toeplitz Matrices by Circulant Matrices

摘要

With every continuous function a on the complex unit circle one can associate a sequence {Tn(a)}infinity n=1 of Toeplitz matrices and a sequence {Cn(a)} infinityn=1 of circulant matrices. By employing some advanced results on the finite sections of Toeplitz operators, we prove asymptotic estimates for the central columns of the matrices Tn-1(a) - Cn -1(a)as n goes to infinity. Our results generalize and sharpen recent results by T. Strohmer and by F.-W. Sun, Y. Jiang, and J. S. Baras, who also discussed the relevancy of the problem in signal processing.