Characterization of classes of polynomial functions (Q5964387)

The authors of the paper under review consider polynomials and generalized polynomials on abelian groups. They call generalized polynomials that are not polynomials \textit{fake polynomials}. For a complex-valued function \(f\) on an abelian group \(G\), the authors denote by \(\tau(f)\) the smallest translation invariant subspace that is closed under pointwise convergence. The authors prove that if \(f\) is a fake polynomial, then the linear span of all additive functions in \(\tau(f)\) is infinite-dimensional.