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Integration of asymptotically almost periodic functions and weak asymptotic almost periodicity

Seria
Rozprawy Matematyczne tom/nr w serii: 279 wydano: 1989
Zawartość
Warianty tytułu
Abstrakty
EN

Summary
We 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.
EN

CONTENTS
0. Introduction...............................................................................5
1. Preliminaries.............................................................................7
2. Weak compactness..................................................................9
3. Weakly asymptotically almost periodic functions.....................14
4. Integrals of asymptotically almost periodic functions...............22
5. References.............................................................................33
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 279
Liczba stron
35
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCLXXIX
Daty
wydano
1989
Twórcy
autor
  • Fachbereich Mathematik, Universität Essen, 4300 Essen 1, German Federal Republic
  • Department of Mathematical Sciences, University or Arkansas, Fayetteville, AR 72701, U.S.A.
Bibliografia
  • [1] L. Amerio and G. Prouse, Almost-periodic Functions and Functional Equations, Van Nostrand, New York 1971.
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  • [20] K. de Leeuw and I. Glicksberg, Applications of almost periodic compactifications. Acta Math. 105 (1961), 63-97.
  • [21] B. M. Levitan and V. Y. Zhikov, Almost Periodic Functions and Differential Equations, Cambridge University Press, Cambridge 1982.
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  • [23] W. Rudin, Weak almost periodic functions and Fourier-Stieltjes transforms, Duke Math. J. 26 (1959), 215-220.
  • [24] W. M. Ruess and C. P. Stegall, Extreme points in duals of operator spaces, Math. Ann. 261 (1982), 535-546.
  • [25] W. M. Ruess and W. H. Summers, Compactness in spaces of vector valued continuous functions and asymptotic almost periodicity. Math. Nachrichten 135 (1988), 7-33.
  • [26] W. M. Ruess and W. H. Summers, Minimal sets of almost periodic motions, Math. Ann. 276 (1986), 145-158.
  • [27] W. M. Ruess and W. H. Summers, Asymptotic almost periodicity and motions of semigroups of operators, J. Linear Algebra Appl. 84 (1986), 335-351; Special Issue "Symposium on Operator Theory", Athens (Greece) 1985.
  • [28] W. M. Ruess and W. H. Summers, Weakly almost periodic semigroups of operators, to appear.
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Języki publikacji
EN
Uwagi
Identyfikator YADDA
bwmeta1.element.zamlynska-a39f3916-3930-46da-a732-42dafdd5da38
Identyfikatory
ISBN
83-01-08945-8
ISSN
0012-3862
Kolekcja
DML-PL
Zawartość książki

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