Demi-linear Analysis II -- Demi-distributions

TL;DR

This paper develops a demi-distributions theory that extends classical distribution concepts, allowing generalizations of differentiation, Fourier transforms, and convolutions within this new framework.

Contribution

It introduces demi-distributions, broadening the scope of distribution theory and enabling generalizations of key operations like differentiation and Fourier analysis.

Findings

Demi-distributions generalize classical distributions.

Differentiation and Fourier transforms are extended to demi-distributions.

Convolution operations are also generalized within this framework.

Abstract

In this paper, we establish a demi-distributions theory which develops the usual distribution theory, in particular, we show that many conclusions as differentiations, Fourier transforms and convolutions can be generalized to the demi-distributions theory.