Multidimensional Widder--Arendt theorem in locally convex spaces

TL;DR

This paper extends the Widder--Arendt theorem to multidimensional functions valued in locally convex spaces, providing new theoretical results even for scalar functions.

Contribution

It formulates and proves a multidimensional Widder--Arendt theorem and its integrated form for functions in locally convex spaces, a novel extension in the field.

Findings

New multidimensional Widder--Arendt theorem established

Integrated form of the theorem proved

Results are novel even for scalar-valued functions

Abstract

In this research article, we formulate and prove multidimensional Widder--Arendt theorem and integrated form of multidimensional Widder--Arendt theorem for functions with values in sequentially complete locally convex spaces. Established results seem to be new even for scalar-valued functions.