Vector-valued almost automorphic distributions and vector-valued almost automorphic ultradistributions

TL;DR

This paper introduces vector-valued almost automorphic distributions and ultradistributions in Banach spaces, providing structural characterizations for these classes.

Contribution

It is the first to define and analyze vector-valued almost automorphic distributions and ultradistributions in the context of Banach spaces.

Findings

Structural characterizations of the new classes

Extension of almost automorphic concepts to vector-valued distributions

Framework applicable in complex Banach spaces

Abstract

In this paper, we introduce the notions of a vector-valued almost automorphic distribution and a vector-valued almost automorphic ultradistribution, working in the framework of complex Banach spaces. We prove several structural characterizations for the introduced classes.