Projective descriptions of spaces of functions and distributions

TL;DR

This paper introduces simplified projective descriptions of classical function and distribution spaces using semi-norms based on classical norms combined with multiplication or convolution, making them easier to analyze.

Contribution

It provides new, simpler semi-norm-based descriptions of function and distribution spaces, improving understanding and potential applications.

Findings

Semi-norms are simpler than supremum-based descriptions.

Descriptions involve classical norms combined with multiplication or convolution.

Facilitates easier analysis of function and distribution spaces.

Abstract

We present projective descriptions of classical spaces of functions and distributions. More precisely, we provide descriptions of these spaces by semi-norms which are defined by a combination of classical norms and multiplication or convolution with certain functions. These seminorms are simpler than the ones given by a supremum over bounded or compact sets.