Large Time Behavior of Finite Difference Schemes for the Transport Equation

In order to study the large time behavior of finite difference schemes for the transport equation, we need to describe the pointwise asymptotic behavior of iterated convolutions for finitely supported sequences indexed on \(\mathbb {Z}\) . In this paper, we investigate this question by presenting the main result of [2] which is a generalization of the so-called local limit theorem in probability theory to complex valued sequences.