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Research articles

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

Marko Kostić

Faculty of Technical Sciences, University of Novi Sad, Trg D. Obradovića 6, 21125 Novi Sad, Serbia

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.

Keywords and phrases: asymptotically almost periodic distributions, asymptotically almost periodic ultradistributions, asymptotically almost automorphic distributions, asymptotically almost automorphic ultradistributions, Banach spaces.

MSC: 46F05, 43A60, 34C27

Received: 13.04.2019

Language: English