A note on recurrent functions (Q1056948)

Let T denote real numbers R or integers Z. By \(RE(T,R^ n)\) and \(D(T,R^ n)\) denote the set of recurrent functions respectively of distal functions \(f: T\to R^ n\). It is known that \(D(T,R^ n)\) is a linear space but \(RE(T,R^ n)\) is not a linear space. It is shown that if \(f\in RE(T,R^ n)-D(T,R^ n)\) then there exist \(g^ 1,g^ 2\in RE(T,R^ n)\) in its hull, such that \(g^ 1-g^ 2\not\in RE(T,R^ n)\).