Asymptotically almost periodic and asymptotically almost automorphic vector-valued generalized functions

TL;DR

This paper introduces new classes of vector-valued ultradistributions that generalize almost periodic and automorphic functions, with applications to analyzing systems of ordinary differential equations.

Contribution

It defines asymptotically almost periodic and automorphic ultradistributions in Banach spaces and explores their properties and applications.

Findings

New definitions of ultradistributions with asymptotic almost periodicity and automorphy.

Analysis of these classes in the context of Banach space-valued distributions.

Applications to systems of ordinary differential equations.

Abstract

The main purpose of this paper is to introduce the notion of an asymptotically almost periodic ultradistribution and asymptotically almost automorphic ultradistribution with values in a Banach space, as well as to further analyze the classes of asymptotically almost periodic and asymptotically almost automorphic distributions with values in a Banach space. We provide some applications of the introduced concepts in the analysis of systems of ordinary differential equations.