International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 1, Pages 23-26
Remarks on extreme eigenvalues of Toeplitz matrices
Department of Mathematical Sciences, Northern Illinois University, DeKalb 60115, Illinois, USA
Received 11 April 1986
Copyright © 1988 Mohsen Pourahmadi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Let be a nonnegative integrable function on , the Toeplitz matrix associated with and its smallest eigenvalue. It is shown that the convergence of to can be exponentially fast even when does not satisfy the smoothness condition of Kac, Murdoch and Szegö (1953). Also a lower bound for corresponding to a large class of functions which do not satisfy this smoothness condition is provided.