Almost Automorphic and Almost Periodic Functions in Abstract Spaces

2001 ◽  
Author(s):  
Gaston M. N’Guerekata
Keyword(s):  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Almost Automorphic ◽  
Abstract Spaces

On Bohr almost periodicity

1986 ◽  
Vol 99 (3) ◽  
pp. 489-493 ◽  
Author(s):  
Paul Milnes
Keyword(s):  
Periodic Function ◽  
Present Author ◽  
Almost Periodic Functions ◽  
Unusual Feature ◽  
Almost Periodicity ◽  
Almost Periodic Function ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Almost Automorphic

AbstractThe first examples of Bohr almost periodic functions that are not almost periodic were given by T. -S. Wu. Later, the present author showed that Bohr almost periodic functions could be distal (and not almost periodic) and even merely minimal. Here it is proved that all Bohr almost periodic functions are minimal. The proof yields an unusual feature about the orbit of a Bohr almost periodic function, one which does not characterize Bohr almost periodic functions, but can be used to show that a Bohr almost periodic function f that is point distal must be distal or, if f is almost automorphic, it must be almost periodic. Some pathologies of Bohr almost periodic functions are discussed.

scholarly journals On some classes of almost periodic functions in abstract spaces

2004 ◽  
Vol 2004 (61) ◽  
pp. 3237-3247 ◽  
Author(s):  
Dariusz Bugajewski ◽  
Gaston M. N'Guérékata
Keyword(s):  
Banach Space ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Superposition Operator ◽  
Periodic Functions ◽  
Partial Differential ◽  
Abstract Spaces

We deal withC(n)-almost periodic functions taking values in a Banach space. We give several properties of such functions, in particular, we investigate their behavior in view of differentiation as well as integration. The superposition operator acting in the space of such functions is also under consideration. Some applications to ordinary as well as partial differential equations are presented. Moreover, we introduce the class of the so-called asymptoticallyC(n)-almost periodic functions and give some of their properties.

scholarly journals The Space of Continuous Periodic Functions Is a Set of First Category inAP(X)

2013 ◽  
Vol 2013 ◽  
pp. 1-3 ◽  
Author(s):  
Zhe-Ming Zheng ◽  
Hui-Sheng Ding ◽  
Gaston M. N'Guérékata
Keyword(s):  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Almost Automorphic ◽  
Almost Automorphic Functions ◽  
First Category ◽  
Set Of First Category ◽  
Automorphic Functions

We prove that the space of continuous periodic functions is a set of first category in the space of almost periodic functions, and we also show that the space of almost periodic functions is a set of first category in the space of almost automorphic functions.

Almost periodic functions

Mathematika ◽  
1955 ◽  
Vol 2 (2) ◽  
pp. 128-131 ◽  
Author(s):  
J. D. Weston
Keyword(s):  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions
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