Multidimensional vector-valued Laplace transform and applications

TL;DR

This paper introduces a new multidimensional vector-valued Laplace transform for functions in locally convex spaces, offering novel theoretical insights and applications to complex integro-differential problems.

Contribution

It develops a comprehensive theory of the multidimensional vector-valued Laplace transform and applies it to abstract Volterra integro-differential inclusions with multiple variables.

Findings

Many results are new even for Banach space-valued functions.

The transform provides new tools for solving multidimensional integro-differential equations.

Applications include analysis of complex Volterra inclusions.

Abstract

In this paper, we introduce and analyze multidimensional vector-valued Laplace transform of functions with values in sequentially complete locally convex spaces. A great number of our results seem to be new even for the functions with values in Banach spaces. We provide several new applications of multidimensional vector-valued Laplace transform to the abstract Volterra integro-differential inclusions with multiple variables, as well.