Notes on eigenvalue distribution of Toeplitz matrices

The author investigates the asymptotic eigenvalue distributions of degenerate Toeplitz matrices. A Toeplitz matrix is degenerate if its rank remains constant while its dimension increases. This type of Toeplitz matrix can arise as the covariance matrix of a degenerated harmonic process. He shows that asymptotically the individual eigenvalues of the degenerate Toeplitz matrix converge to the amplitude of corresponding harmonic components. This is a stronger result than previously developed