On the Non-uniqueness of the Decomposition of Weighted Pseudo Almost Periodic Functions

2012 ◽  
pp. 43-46
Author(s):  
Gaston M. N’Guérékata
Keyword(s):  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Pseudo Almost Periodic Functions ◽  
Pseudo Almost Periodic

scholarly journals Some Properties of Weighted Pseudo almost Periodic Functions

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Zhe-Ming Zheng ◽  
Hui-Sheng Ding ◽  
Gaston M. N’Guérékata
Keyword(s):  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Proper Subspace ◽  
Equivalent Definition ◽  
Classical Space ◽  
Pseudo Almost Periodic Functions ◽  
Close Relationship ◽  
Pseudo Almost Periodic ◽  
Asymptotically Almost Periodic

Several interesting and new properties of weighted pseudo almost periodic functions are established. Firstly, we obtain an equivalent definition for weighted pseudo almost periodic functions, which shows a close relationship between asymptotically almost periodic functions and weighted pseudo almost periodic functions; secondly, we prove that the space of asymptotically almost periodic functions is always a proper subspace of the space of weighted pseudo almost periodic functions; thirdly, we show that under some cases, the space of weighted pseudo almost periodic functions equals the classical space of pseudo almost periodic functions.

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