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 Diophantine approximations and almost periodic functions

2017 ◽  
Vol 50 (1) ◽  
pp. 100-104
Author(s):  
Adam Nawrocki
Keyword(s):  
Periodic Function ◽  
Asymptotic Behaviour ◽  
Almost Periodic Functions ◽  
Almost Periodic Function ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Polynomial Type ◽  
Diophantine Approximations ◽  
Polynomial Estimation

Abstract In this paper we investigate the asymptotic behaviour of the classical continuous and unbounded almost periodic function in the Lebesgue measure.Using diophantine approximations we show that this function can be estimated by functions of polynomial type and we give the best polynomial estimation.

Compactness and Almost Periodicity of Multipliers

1983 ◽  
Vol 26 (1) ◽  
pp. 58-62 ◽  
Author(s):  
G. Crombez
Keyword(s):  
Large Class ◽  
Function Spaces ◽  
Almost Periodic Functions ◽  
Almost Periodicity ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Weakly Compact ◽  
Banach Function Spaces ◽  
General Method

AbstractThe question as to the existence of nontrivial compact or weakly compact multipliers between spaces of functions on groups has been investigated for several years. Until now, however, no general method which is applicable to a large class of function spaces seems to be knownIn this paper we prove that the existence of nontrivial compact multipliers between Banach function spaces on which a group acts is related to the existence of nonzero almost periodic functions.

On Weakly Almost-Periodic Families of Linear Operators

1975 ◽  
Vol 18 (1) ◽  
pp. 81-85
Author(s):  
Aribindi Satyanarayan Rao
Keyword(s):  
Periodic Function ◽  
Linear Operators ◽  
Almost Periodicity ◽  
Almost Periodic Function ◽  
Almost Periodic ◽  
Weakly Almost Periodic ◽  
Periodic Family

AbstractIn this note first the weak almost-periodicity of the action of a weakly almost-periodic family of linear operators on an almost-periodic function is established. Then an application of this result is given.

scholarly journals Notes on almost-periodicity in topological vector spaces

1986 ◽  
Vol 9 (1) ◽  
pp. 201-204 ◽  
Author(s):  
Gaston Mandata N'guérékata
Keyword(s):  
Differential Equations ◽  
Almost Periodic Functions ◽  
Vector Spaces ◽  
Almost Periodicity ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Topological Vector Spaces ◽  
Abstract Differential Equations

A study is made of almost-periodic functions in topological vector spaces with applications to abstract differential equations.

scholarly journals Denjoy-Bochner almost periodic functions

1984 ◽  
Vol 37 (2) ◽  
pp. 205-222 ◽  
Author(s):  
B. K. Pal ◽  
S. N. Mukhopadhyay
Keyword(s):  
Integrable Function ◽  
Almost Periodic Functions ◽  
Almost Periodicity ◽  
Almost Periodic ◽  
Bochner Integral ◽  
Periodic Functions ◽  
Integrable Functions

AbstractThe special Denjoy-Bochner integral (the D*B-integral) which are generalisations of Lebesgue-Bochner integral are discussed in [7, 6, 5]. Just as the concept of numerical almost periodicity was extended by Burkill [3] to numerically valued D*- or D-integrable function, we extend the concept of almost periodicity for Banach valued function to Banach valued D*B-integrable function. For this purpose we introduce as in [3] a distance in the space of all D*B-integrable functions with respect to which the D*B-almost periodicity is defined. It is shown that the D*B-almost periodicity shares many of the known properties of the almost periodic Banach valued function [1, 4].

THE CONNECTION BETWEEN PSEUDO ALMOST PERIODIC FUNCTIONS DEFINED ON TIME SCALES AND ON THE REAL LINE

2017 ◽  
Vol 95 (3) ◽  
pp. 482-494 ◽  
Author(s):  
CHAO-HONG TANG ◽  
HONG-XU LI
Keyword(s):  
Time Scales ◽  
Almost Periodic Functions ◽  
Almost Periodic Function ◽  
Almost Periodic ◽  
Necessary And Sufficient Condition ◽  
Periodic Functions ◽  
Pseudo Almost Periodic Functions ◽  
Necessary And Sufficient ◽  
Pseudo Almost Periodic ◽  
Uniformly Continuous

A necessary and sufficient condition for a continuous function $g$ to be almost periodic on time scales is the existence of an almost periodic function $f$ on $\mathbb{R}$ such that $f$ is an extension of $g$. Our aim is to study this question for pseudo almost periodic functions. We prove the necessity of the condition for pseudo almost periodic functions. An example is given to show that the sufficiency of the condition does not hold for pseudo almost periodic functions. Nevertheless, the sufficiency is valid for uniformly continuous pseudo almost periodic functions. As applications, we give some results on the connection between the pseudo almost periodic (or almost periodic) solutions of dynamic equations on time scales and of the corresponding differential equations.

scholarly journals Generalized Almost Periodicity in Lebesgue Spaces with Variable Exponents

Mathematics ◽  
2020 ◽  
Vol 8 (6) ◽  
pp. 928 ◽  
Author(s):  
Marko Kostić ◽  
Wei-Shih Du
Keyword(s):  
Banach Spaces ◽  
Differential Inclusions ◽  
Almost Periodic Functions ◽  
Almost Periodicity ◽  
Variable Exponents ◽  
Almost Periodic ◽  
Periodic Functions ◽  
Lebesgue Spaces ◽  
Recurrent Functions ◽  
Convolution Products

In this paper, we introduce and analyze Stepanov uniformly recurrent functions, Doss uniformly recurrent functions and Doss almost-periodic functions in Lebesgue spaces with variable exponents. We investigate the invariance of these types of generalized almost-periodicity in Lebesgue spaces with variable exponents under the actions of convolution products, providing also some illustrative applications to the abstract semilinear integro-differential inclusions in Banach spaces.

scholarly journals Distribution of Small Values of Bohr Almost Periodic Functions with Bounded Spectrum

2019 ◽  
pp. 571-578
Author(s):  
Wayne M. Lawton
Keyword(s):  
Periodic Function ◽  
Riemann Hypothesis ◽  
Mahler Measure ◽  
Trigonometric Polynomials ◽  
Almost Periodic Function ◽  
Almost Periodic ◽  
Periodic Functions ◽  
The Mean ◽  
Relationship Of ◽  
The Relationship

For f a nonzero Bohr almost periodic function on R with a bounded spectrum we proved there exist Cf > 0 and integer n > 0 such that for every u > 0 the mean measure of the set f x : jf(x)j < u g is less than Cf u1=n: For trigonometric polynomials with n + 1 frequencies we showed that Cf can be chosen to depend only on n and the modulus of the largest coefficient of f: We showed this bound implies that the Mahler measure M(h); of the lift h of f to a compactification G of R; is positive and discussed the relationship of Mahler measure to the Riemann Hypothesis

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