On Difference Operators and their Factorization
Patrick J. Browne, Rodney Nillsen · Canadian Journal of Mathematics · 1983
Throughout this paper A will be used to denote a given set and g a permutation of it. We shall assume that there is a subset C ⊆ A so that 1 Here Z denotes the set of integers. For x ∈ A it now follows that there is an unique α(x) ∈ Z so that 2 and then also In general we shall be concerned with solving the following equation for u 3 where pi, n ≤ i ≤ r, and v are given real valued functions on A and pnpr does not vanish on A. For B ⊆ A, F(B) will denote the set of all real valued functions defined on B.