Liouvillian solutions of linear difference–differential equations

For a field k with an automorphism σ and a derivation δ, we introduce the notion of Liouvillian solutions of linear difference–differential systems {σ(Y)=AY,δ(Y)=BY} over k and characterize the existence of Liouvillian solutions in terms of the Galois group of the systems. In the forthcoming paper, we will propose an algorithm for deciding if linear difference–differential systems of prime order have Liouvillian solutions.