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.
Ford, N., Savostyanov, D., & Zamarashkin, N. (2014). On the Decay of the Elements of Inverse Triangular Toeplitz Matrices. SIAM Journal on Matrix Analysis and Applications, 35(4), 1288-1302. https://doi.org/10.1137/130931734