scholarly journals On Hilbert dynamical systems

2011 ◽  
Vol 32 (2) ◽  
pp. 629-642 ◽  
Author(s):  
ELI GLASNER ◽  
BENJAMIN WEISS
Keyword(s):  
Dynamical Systems ◽  
Periodic Function ◽  
Harmonic Analysis ◽  
Dual Group ◽  
Almost Periodic Function ◽  
Almost Periodic ◽  
Norm Closure ◽  
Weakly Almost Periodic ◽  
Stieltjes Transforms

AbstractReturning to a classical question in harmonic analysis, we strengthen an old result of Walter Rudin. We show that there exists a weakly almost periodic function on the group of integers ℤ which is not in the norm-closure of the algebra B(ℤ) of Fourier–Stieltjes transforms of measures on the dual group $\hat {\mathbb {Z}}=\mathbb {T}$, and which is recurrent. We also show that there is a Polish monothetic group which is reflexively but not Hilbert representable.

On the almost periodic solution of an abstract diffferential equation

1974 ◽  
Vol 18 (2) ◽  
pp. 252-256
Author(s):  
Aribindi Satyanarayan Rao
Keyword(s):  
Differential Equation ◽  
Periodic Solution ◽  
Periodic Function ◽  
Bounded Solution ◽  
Almost Periodic Solution ◽  
Almost Periodic Function ◽  
Almost Periodic ◽  
Abstract Differential Equation ◽  
Weakly Almost Periodic

Abstract: Under certain suitable conditions, the Stepanov-bounded solution of an abstract differential equation corresponding to a Stepanov almost periodic function is strongly (weakly) almost periodic.

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 Compactifications of semitopological semigroups II

1976 ◽  
Vol 22 (2) ◽  
pp. 129-134 ◽  
Author(s):  
Paul Milnes
Keyword(s):  
Topological Group ◽  
Periodic Function ◽  
Almost Periodic Function ◽  
Almost Periodic ◽  
Invariant Metric ◽  
Locally Compact ◽  
Weakly Almost Periodic ◽  
Left And Right ◽  
Uniformly Continuous

AbstractCorrecting some “proofs” given in an earlier paper of the same title, we prove here, among other things, that, if S is a subgroup of a topological group that is complete in a left invariant metric or locally compact, then every weakly almost periodic function on S is (left and right) uniformly continuous. We also prove a theorem related to results of R. B. Burckel and of W. W. Comfort and K. A. Ross: a topological group is pseudocompact if and only if WAP(G) = C(G).

EXPONENTIAL CONVERGENCE OF CELLULAR NEURAL NETWORKS WITH CONTINUOUSLY DISTRIBUTED DELAYS

2007 ◽  
Vol 17 (12) ◽  
pp. 4403-4408
Author(s):  
BINGWEN LIU ◽  
ZHAOHUI YUAN
Keyword(s):  
Neural Networks ◽  
Periodic Function ◽  
Exponential Convergence ◽  
Sufficient Conditions ◽  
Cellular Neural Networks ◽  
Distributed Delays ◽  
Almost Periodic Function ◽  
Almost Periodic ◽  
Periodic Coefficients ◽  
All Solutions

In this paper the convergence behavior of delayed cellular neural networks without almost periodic coefficients are considered. Some sufficient conditions are established to ensure that all solutions of the networks converge exponentially to an almost periodic function, which are new, and also complement previously known results.

scholarly journals On the Spectrum of almost periodic solutions of an abstract differential equation

1974 ◽  
Vol 18 (4) ◽  
pp. 385-387
Author(s):  
Aribindi Satyanarayan Rao ◽  
Walter Hengartner
Keyword(s):  
Differential Equation ◽  
Banach Space ◽  
Periodic Solution ◽  
Linear Operator ◽  
Periodic Function ◽  
Almost Periodic Solution ◽  
Almost Periodic Solutions ◽  
Almost Periodic Function ◽  
Almost Periodic ◽  
Abstract Differential Equation

AbstractIf a linear operator A in a Banach space satisfies certain conditions, then the spectrum of any almost periodic solution of the differential equation u′ = Au + f is shown to be identical with the spectrum of f, where f is a Stepanov almost periodic function.

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