scholarly journals CONTINUOUS MAPPINGS OF ALMOST AUTOMORPHIC AND ALMOST PERIODIC FUNCTIONS

1964 ◽  
Vol 52 (4) ◽  
pp. 907-910 ◽  
Author(s):  
S. Bochner
Keyword(s):  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Almost Automorphic ◽  
Continuous Mappings

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 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.

(VC)(n)-ALMOST PERIODIC FUNCTIONS

1999 ◽  
Vol 32 (2) ◽  
Author(s):  
Stanislaw Stoinski
Keyword(s):  
Almost Periodic Functions ◽  
Almost Periodic ◽  
Periodic 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

scholarly journals Almost periodic functions and hyperbolic counting

2018 ◽  
Vol 14 (09) ◽  
pp. 2343-2368
Author(s):  
Giacomo Cherubini
Keyword(s):  
Asymptotic Variance ◽  
Limiting Distribution ◽  
Almost Periodic Functions ◽  
Specific Class ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Circle Problem

We prove the existence of asymptotic moments and an estimate on the tails of the limiting distribution for a specific class of almost periodic functions. Then we introduce the hyperbolic circle problem, proving an estimate on the asymptotic variance of the remainder that improves a result of Chamizo. Applying the results of the first part we prove the existence of limiting distribution and asymptotic moments for three functions that are integrated versions of the remainder, and were considered originally (with due adaptations to our settings) by Wolfe, Phillips and Rudnick, and Hill and Parnovski.

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