Exponential semi-polynomials on semigroups are natural generalizations of exponential polynomials on groups. We show that several of the standard properties of exponential polynomials on groups also hold for exponential semi-polynomials on semigroups. The main result is that for topological commutative monoids S belonging to a certain class, a function in C(S) is an exponential semi-polynomial if and only if it is contained in a finite dimensional translation invariant linear subspace. We also show that some standard results about polynomials on commutative semigroups are in fact valid on all semigroups.

中文翻译：

---

指数半多项式及其在半群上的表征

半群上的指数半多项式是群上指数多项式的自然推广。我们证明了群上的指数多项式的几个标准性质也适用于半群上的指数半多项式。主要结果是，对于属于某一类的拓扑交换幺半群S ， C ( S ) 中的函数是指数半多项式当且仅当它包含在有限维平移不变线性子空间中。我们还表明，有关交换半群多项式的一些标准结果实际上对所有半群都有效。