Generalized polynomials on semigroups - Ebanks, Bruce (Annales Mathematicae Silesianae, 2024)
This article has two main parts. In the first part we show that some of the basic theory of generalized polynomials on commutative semigroups can be extended to all semigroups. In the second part we show that if a sub-semigroup S of a group G generates G in the sense that G = S·S−1, then a generalized polynomial on S with values in an Abelian group H can be extended to a generalized polynomial on G into H. Finally there is a short discussion of the extendability of exponential functions and generalized exponential polynomials.