Abstract
Vector-valued pseudo almost periodic functions are defined and their properties are investigated. The vector-valued functions contain many known functions as special cases. A unique decomposition theorem is given to show that a vector-valued pseudo almost periodic function is a sum of an almost periodic function and an ergodic perturbation.
Similar content being viewed by others
References
L. Amerio and G. Prouse: Almost-Periodic Functions and Functional Equations. Van Nostrand, New York, 1971.
J.F. Berglund, H.D. Junghenn and P. Milnes: Analysis on Semigroups: Function Spaces, Compactifications, Representations. Wiley, New York, 1989.
A. S. Besicovitch: Almost Periodic Functions. Dover, New York, 1954.
H.A. Bohr: Almost Periodic Functions. Chelsea, New York, 1951.
C. Corduneanu: Almost Periodic Functions. Chelsea, New York, 2nd ed., 1989.
K. de Leeuw and I. Glicksberg: Applications of almost periodic compactifications. Acta Math. 105 (1961), 63–97.
S. Goldberg and P. Irwin: Weakly almost periodic vector valued functions. Dissertationes Math. 157 (1979).
B. M. Levitan and V. V. Zhikov: Almost periodic functions and differential equations. Cambridge University Press, New York, 1982.
P. Milnes: On vector-valued weakly almost periodic functions. J. London Math. Soc. (2) 22 (1980), 467–472.
W.M. Ruess and W.H. Summers: Compactness in spaces of vector valued continuous functions and asymptotic almost periodicity. Math. Nachr. 135 (1988), 7–33.
W.M. Ruess and W.H. Summers: Integration of asymptotically almost periodic functions and weak asymptotic almost periodicity. Dissertationes Math. 279 (1989).
S. Zaidman: Almost-Periodic Functions in Abstract Spaces. Pitman, London, 1985.
C. Zhang: Pseudo almost periodic solutions of some differential equations. J. Math. Anal. Appl. 181 (1994), 62–76.
C. Zhang: Pseudo almost periodic solutions of some differential equations, II. J. Math. Anal. Appl. 192 (1995), 543–561.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Zhang, C. Vector-valued pseudo almost periodic functions. Czechoslovak Mathematical Journal 47, 385–394 (1997). https://doi.org/10.1023/A:1022492014464
Issue Date:
DOI: https://doi.org/10.1023/A:1022492014464