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.

Continuity properties of compact right topological groups

1979 ◽  
Vol 86 (3) ◽  
pp. 427-435 ◽  
Author(s):  
Paul Milnes
Keyword(s):  
Almost Periodic ◽  
Periodic Functions ◽  
Topological Groups ◽  
Almost Automorphic ◽  
Almost Automorphic Function ◽  
Almost Automorphic Functions ◽  
Continuity Properties ◽  
Enveloping Semigroups ◽  
The One ◽  
Automorphic Functions

AbstractCompact right topological groups appear naturally in topological dynamics. Some continuity properties of the one arising as an enveloping semigroup from the distal function are considered here (and, by way of comparison, the enveloping semigroups arising from two almost automorphic functions are discussed). The continuity properties are established either explicitly or by citing a theorem which is proved here and gives some characterizations of almost periodic functions. One characterization is proved using the result (essentially due to W. A. Veech) that a distal, almost automorphic function is almost periodic. A proof of this last result is also given.

scholarly journals (&omega,c)- PSEUDO ALMOST PERIODIC FUNCTIONS, (&omega,c)- PSEUDO ALMOST AUTOMORPHIC FUNCTIONS AND APPLICATIONS

2021 ◽  
pp. 165
Author(s):  
Mohammed Taha Khalladi ◽  
Marko Kostić ◽  
Abdelkader Rahmani ◽  
Daniel Velinov
Keyword(s):  
Banach Spaces ◽  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
First Order ◽  
Almost Automorphic Functions ◽  
Pseudo Almost Periodic Functions ◽  
Pseudo Almost Automorphic ◽  
Pseudo Almost Periodic ◽  
Automorphic Functions

In this paper, we introduce the classes of $(\omega, c)$-pseudo almost periodicfunctions and $(\omega, c)$-pseudo almost automorphicfunctions. These collections include $(\omega, c)$-pseudo periodicfunctions, pseudo almost periodic functions and their automorphic analogues.We present an application to the abstract semilinear first-order Cauchy inclusions in Banach 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 Almost Automorphic Functions on the Quantum Time Scale and Applications

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Yongkun Li
Keyword(s):  
Time Scales ◽  
Time Scale ◽  
Dynamic Equations ◽  
Almost Periodic ◽  
Almost Automorphic ◽  
Almost Automorphic Functions ◽  
Quantum Time ◽  
Almost Periodic Time Scales ◽  
Automorphic Functions ◽  
General Time

We first propose two types of concepts of almost automorphic functions on the quantum time scale. Secondly, we study some basic properties of almost automorphic functions on the quantum time scale. Then, we introduce a transformation between functions defined on the quantum time scale and functions defined on the set of generalized integer numbers; by using this transformation we give equivalent definitions of almost automorphic functions on the quantum time scale; following the idea of the transformation, we also give a concept of almost automorphic functions on more general time scales that can unify the concepts of almost automorphic functions on almost periodic time scales and on the quantum time scale. Finally, as an application of our results, we establish the existence of almost automorphic solutions of linear and semilinear dynamic equations on the quantum time scale.

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