On the Decay of the Elements of Inverse Triangular Toeplitz Matrices

We consider half-infinite triangular Toeplitz matrices with slow decay of the elements and prove under a monotonicity condition that the elements of the inverse matrix, as well as the elements of the fundamental matrix, decay to zero. We provide a quantitative description of the decay of the fundamental matrix in terms of p-norms. The results add to the classical results of Jaffard and Vecchio and are illustrated by numerical examples.