Characterization of almost maximally almost-periodic groups

Let G be an Abelian group. We prove that a group G admits a Hausdorff group topology τ such that the von Neumann radical n(G,τ) of (G,τ) is non-trivial and finite iff G has a non-trivial finite subgroup. If G is a topological group, then n(n(G))≠n(G) if and only if n(G) is not dually embedded. In particular, n(n(Z,τ))=n(Z,τ) for any Hausdorff group topology τ on Z.     

Minimally almost periodic totally disconnected groups

In this paper we prove that every closed noncompact group of isometries of a homogeneous tree which acts transitively on the tree boundary contains a normal closed cocompact subgroup which is minimally almost periodic. Moreover we prove that is a topologically simple group.

     

Weakly almost periodic functions on semisimple Lie groups

IfG is a semisimple analytic group with finite center, it is proved thatG admits only the “obvious” weakly almost periodic functions. The analysis yields also an intrinsic proof of Moore's ergodicity theorem [7].     

概周期系统概周期解的存在唯一性

运用Ｌｉａｐｕｎｏｖ函数，研究了概周期系统概周期解的存在唯一性，得到了一个方便应用的判定定理．     

Herz-Schur multipliers and weakly almost periodic functions on locally compact groups

For a locally compact group and , let be the Herz-Figà-Talamanca algebra and the Herz-Schur multipliers of , and the multipliers of . Let be the algebra of continuous weakly almost periodic functions on . In this paper, we show that (1), if is a noncompact nilpotent group or a noncompact [IN]-group, then contains a linear isometric copy of ; (2), for a noncommutative free group is a proper subset of .

     

Asymptotically almost periodic,almost periodic and pseudo-almost periodic mild solutions for neutral differential equations

In this paper we establish the existence and uniqueness of almost periodic, asymptotically almost periodic and pseudo-almost periodic mild solutions for neutral differential equations in Banach spaces.     

Asymptotically almost periodic and almost periodic solutions for partial neutral differential equations

In this work we study the existence of almost periodic and asymptotically almost periodic solutions for partial neutral functional differential equations with unbounded delay.     

Asymptotically almost periodic distributions

In this work we extend to the space of Schwartz' distributions the notion of asymptotic almost periodicity of M. Frechet. The main justification for the introduction of this concept is the fact that for certain differential equations in distributions the existence of an asymptotic almost periodic (distribution) solution implies the existence of an almost periodic (distribution) solution, as an example shows     

Completely almost periodic functionals

Using the notion of complete compactness introduced by H.  Saar, we define completely almost periodic functionals on completely contractive Banach algebras. We show that, if (M, Γ) is a Hopf–von Neumann algebra with M injective, then the space of completely almost periodic functionals on M _* is a C*-subalgebra of M.     

Measure-valued almost periodic functions

We consider Stepanov almost periodic functions μ ∈ ranging in the metric space of Borel probability measures on a complete separable metric space is equipped with the Prokhorov metric). The main result is as follows: a function , belongs to if and only if for each bounded continuous function , the function is Stepanov almost periodic (of order 1) and

On almost reducible systems with almost periodic coefficients

Let x=A(t)x be a system of two linear ordinary differential equations with almost periodic coefficients. Then there exists for any positive ε an almost reducible system of equations x=B(t)x with almost periodic coefficients and such that sup ∥A(t)?B (t)∥<ε.-∞相似文献   

Fields of almost periodic sequences

Let F((x)) be the field of formal power series over the field with two elements F. We classify all quadratic elements in F((x)) which are almost periodic, the Morse-Hedlund sequence being a special case. We also give some results for higher-degree almost periodic elements.     

Approximation of almost periodic functions by periodic ones

It is not the purpose of this paper to construct approximations but to establish a class of almost periodic functions which can be approximated, with an arbitrarily prescribed accuracy, by continuous periodic functions uniformly on =(+).     

Characterizations of almost periodic homeomorphisms

In this paper we study recurrent and almost periodic homeomorphisms on the Euclidean space Rm; we give conditions under which recurrent implies periodic. On the other hand we give properties of elements of compact groups of diffeomorphisms on manifolds.