An extension of a result of Szegő on eigenvalues of Toeplitz matrices (Q877901)

The authors of the paper under review study the asymptotic behavior of eigenvalues of Toeplitz matrices. In particular, they find asymptotic behavior of the eigenvalues of Toeplitz matrices \(T_N(g)\), with \(g(e^{i\theta})=(1-\cos\theta)^\alpha f(e^{i\theta})\), where \(f\) is a regular function. In particular, they obtain the order of the smallest and the largest eigenvalues.