SummaryWe resolve the question as to when an asymptotically almost periodic function with values in a Banach space has an asymptotically almost periodic integral. Further, we characterize the weakly relatively compact sets in spaces of vector valued continuous functions and use the resulting criteria to investigate the relationship between weak almost periodicity in the sense of Eberlein and the parallel notion utilized by Amerio in his approach to extending the classical Bohl-Bohr integration theorem. One consequence is the discovery of an unexpected connection between Eberlein weak almost periodicity and the asymptotic almost periodicity of integrals. We also apply our methods to investigate periodicity properties inherited by integrals of functions which are only asymptotically almost periodic in a weak sense.
CONTENTS0. Introduction...............................................................................51. Preliminaries.............................................................................72. Weak compactness..................................................................93. Weakly asymptotically almost periodic functions.....................144. Integrals of asymptotically almost periodic functions...............225. References.............................................................................33
@book{bwmeta1.element.zamlynska-a39f3916-3930-46da-a732-42dafdd5da38,
author = {W. M. Ruess and W. H. Summers},
title = {Integration of asymptotically almost periodic functions and weak asymptotic almost periodicity},
series = {GDML\_Books},
publisher = {Instytut Matematyczny Polskiej Akademi Nauk},
address = {Warszawa},
year = {1989},
zbl = {0668.43005},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.zamlynska-a39f3916-3930-46da-a732-42dafdd5da38}
}
W. M. Ruess; W. H. Summers. Integration of asymptotically almost periodic functions and weak asymptotic almost periodicity. GDML_Books (1989), http://gdmltest.u-ga.fr/item/bwmeta1.element.zamlynska-a39f3916-3930-46da-a732-42dafdd5da38/