Remarks on extreme eigenvalues of Toeplitz matrices Academic Article uri icon

abstract

  • Letfbe a nonnegative integrable function on[,],Tn(f)the(n+1)(n+1)Toeplitz matrix associated withfand1,nits smallest eigenvalue. It is shown that the convergence of1,ntominf(0)can be exponentially fast even whenfdoes not satisfy the smoothness condition of Kac, Murdoch and Szeg (1953). Also a lower bound for1,ncorresponding to a large class of functions which do not satisfy this smoothness condition is provided.

published proceedings

  • International Journal of Mathematics and Mathematical Sciences

author list (cited authors)

  • Pourahmadi, M.

citation count

  • 8

complete list of authors

  • Pourahmadi, Mohsen

publication date

  • January 1988