Multi-dimensional Besicovitch almost periodic type functions and applications

TL;DR

This paper studies multi-dimensional Besicovitch almost periodic functions, clarifies their structural properties, introduces a new notion of Besicovitch-Doss almost periodicity, and applies these concepts to integro-differential and partial differential equations.

Contribution

It introduces and analyzes multi-dimensional Besicovitch almost periodic functions and their properties, including a new notion of Besicovitch-Doss almost periodicity, with applications to differential equations.

Findings

Structural properties of Besicovitch almost periodic functions clarified

Introduction of Besicovitch-Doss almost periodicity in multiple dimensions

Applications to Volterra integro-differential and PDEs demonstrated

Abstract

In this paper, we analyze multi-dimensional Besicovitch almost periodic type functions. We clarify the main structural properties for the introduced classes of Besicovitch almost periodic type functions, explore the notion of Besicovitch-Doss almost periodicity in the multi-dimensional setting, and provide some applications of our results to the abstract Volterra integro-differential equations and the partial differential equations.