International Journal of Mathematics and Mathematical Sciences
Volume 11 (1988), Issue 1, Pages 23-26

Remarks on extreme eigenvalues of Toeplitz matrices

Mohsen Pourahmadi

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 f be a nonnegative integrable function on [π,π], Tn(f) the (n+1)×(n+1) Toeplitz matrix associated with f and λ1,n its smallest eigenvalue. It is shown that the convergence of λ1,n to minf(0) can be exponentially fast even when f does not satisfy the smoothness condition of Kac, Murdoch and Szegö (1953). Also a lower bound for λ1,n corresponding to a large class of functions which do not satisfy this smoothness condition is provided.