Axiomatic Theory of Distributions

TL;DR

This paper introduces a simple axiomatic framework for distributions and their derivatives, extending Schwartz's concepts, and proposes a generalized axiomatic approach to these mathematical objects.

Contribution

It formulates simple axiomatic definitions for distributions and derivatives, and generalizes these concepts within an axiomatic framework.

Findings

Axiomatic definitions for distributions and derivatives are established.

A generalized concept of distributions is proposed.

The framework simplifies understanding of distribution theory.

Abstract

In this monograph, very simple axiomatic definitions to the L. Schwartz' concepts of distribution and derivative of a distribution are formulated. Beyond this, a kind of generalization of that concepts is propose and corresponding axiomatic definitions are presented.