Abstract :
We characterize continuous linear endomorphisms which commute with a fixed Carlitz difference operator on the space of continuous Fq-linear functions defined over the completion of Fq[T] in terms of a bounded sequence, which is closely related to hyper-differential operators. This leads us to establish that such an endomorphism has a unique expansion with respect to the Carlitz difference operators and then the solution space of difference equations is explicitly described.
