Uniqueness sequences for multidimensional vector-valued Laplace transform

TL;DR

This paper investigates the conditions under which multidimensional vector-valued Laplace transforms are uniquely determined by their sequences, establishing links to the one-dimensional case and providing examples and open problems.

Contribution

It introduces new relationships between one-dimensional and multidimensional uniqueness sequences for Laplace transforms, expanding understanding in this area.

Findings

Established fundamental relationships between 1D and multidimensional uniqueness sequences.

Provided illustrative examples demonstrating these relationships.

Outlined open problems and observations for future research.

Abstract

In this research article, we consider the uniqueness sequences for multidimensional vector-valued Laplace transform. We establish the fundamental relationships between uniqueness sequences for one-dimensional Laplace transform and uniqueness sequences for multidimensional Laplace transform. We also provide several illustrative examples, open problems and useful observations in the above direction.