Reconstruction of the one-dimensional thick distribution theory

Abstract

The theory of thick distributions (both in dimension 1 and in higher dimensions) was constructed in recent years [7, 27]. However this theory of distributions with one thick point in dimension one is very different from that in higher dimensions. In this paper the author uses the language of asymptotic analysis to reconstruct the 1-dimensional thick distribution theory and to incorporate it into the framework of the higher-dimensional thick distribution theory. Some new concepts and interesting results appear in this paper from viewing singular functions in a different way.