Discrete analysis in commutative rings (Q1206987)

The present paper is a direct sequel of the work ``A Theory of Discrete Analysis'' [this J. 169, No. 2, 374-390 (1992; Zbl 0781.46030)] of the author where a limit-free theory of analysis was introduced in the class of abelian groups. Here this study is continued within the class of commutative rings. One of the main results of this paper is: the integral completion of the convolution ring \(\mathbb{P}\) under the \(\Delta\)-structure \({\mathcal P}\) is isomorphic to the space of complex periodic distributions of a given period \(T\).