Almost periodic functions and representations in locally convex spaces

2005 ◽  
Vol 60 (3) ◽  
pp. 489-557 ◽  
Author(s):  
Alexander I Shtern
Keyword(s):  
Almost Periodic Functions ◽  
Locally Convex Spaces ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Locally Convex ◽  
Convex Spaces

scholarly journals Asymptotic Almost Periodic Functions with Range in a Topological Vector Space

2013 ◽  
Vol 2013 ◽  
pp. 1-7
Author(s):  
Liaqat Ali Khan ◽  
Saud M. Alsulami
Keyword(s):  
Vector Space ◽  
Topological Vector Space ◽  
Almost Periodic Functions ◽  
Almost Periodicity ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Range Space ◽  
Finite Dimensional ◽  
Locally Convex ◽  
Dimensional Range

The notion of asymptotic almost periodicity was…first introduced by Fréchet in 1941 in the case of…finite dimensional range spaces. Later, its extension to the case of Banach range spaces and locally convex range spaces has been considered by several authors. In this paper, we have generalized the concept of asymptotic almost periodicity to the case where the range space is a general topological vector space, not necessarily locally convex. Our results thus widen the scope of applications of asymptotic almost periodicity.

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