On a space of rapidly decreasing infinitely differentiable functions on an unbounded convex set in ${\mathbb R}^n$ and its dual

TL;DR

This paper characterizes continuous linear functionals on a space of rapidly decreasing smooth functions on an unbounded convex set in ^n using Fourier-Laplace transforms, extending understanding of functional analysis in this context.

Contribution

It provides a new description of linear continuous functionals on this function space via Fourier-Laplace transforms, expanding the theoretical framework.

Findings

Characterization of linear functionals through Fourier-Laplace transform

Extension of functional analysis to unbounded convex sets

Enhanced understanding of dual spaces in this context

Abstract

Description of linear continuous functionals on a space of rapidly decreasing infinitely differentiable functions on an unbounded closed convex set in $\mathbb R^n$ in terms of their Fourier-Laplace transform is obtained.