1. Definitions and examples

The article is divided into two parts: the first deals with the point of view according to which a linear difference equation is interpreted as a linear application of the space of complex-valued sequences ${\mathrm{C}}^{\mathrm{N}}$ into itself. The second part considers a linear difference equation as acting on complex-valued functions (the theory is more difficult and has only been available algorithmically for a few years).

We have chosen to highlight current methods for studying this theory. We have been guided by a concern for motivation, and refer to the most recent documents for the necessarily more technical developments. As a result, we have departed considerably from the classic...