Non-standard representations of distributions. II (Q1173746)

This paper is a continuation of the previous one [ibid. 25, No. 4, 805- 824 (1988; Zbl 0724.46040)]. Its aim is to represent the space \({\mathcal S}'(\mathbb{R})\) of tempered distributions on \(\mathbb{R}\), the space \({\mathcal S}(\mathbb{R})\) of rapidly decreasing functions on \(\mathbb{R}\) and the Fourier transformation on the space \({\mathcal S}'(\mathbb{R})\) by using a kind of standardization of functions and transformations on a \(*\)-finite subset of a lattice with infinitesimal mesh.