共查询到20条相似文献,搜索用时 31 毫秒
1.
D. Junghenn 《Semigroup Forum》2008,66(2):328-336
Abstract. Let
be a semidirect product of semitopological semigroups S and T . If S and T act on topological spaces X and Y , respectively, then under suitable conditions there is a natural action of
on X × Y . In this paper we characterize the almost periodic and strongly almost periodic compactification of the flow
,
in terms of related compactifications of (S,X) and (T,Y) . 相似文献
2.
Yevhen Zelenyuk 《Topology and its Applications》2007,154(2):339-357
A topological space X is called almost maximal if it is without isolated points and for every x∈X, there are only finitely many ultrafilters on X converging to x. We associate with every countable regular homogeneous almost maximal space X a finite semigroup Ult(X) so that if X and Y are homeomorphic, Ult(X) and Ult(Y) are isomorphic. Semigroups Ult(X) are projectives in the category F of finite semigroups. These are bands decomposing into a certain chain of rectangular components. Under MA, for each projective S in F, there is a countable almost maximal topological group G with Ult(G) isomorphic to S. The existence of a countable almost maximal topological group cannot be established in ZFC. However, there are in ZFC countable regular homogeneous almost maximal spaces X with Ult(X) being a chain of idempotents. 相似文献
3.
Let X, X1, X2, … be i.i.d. random variables with nondegenerate common distribution function F, satisfying EX = 0, EX2 = 1. Let Xi and Mn = max{Xi, 1 ≤ i ≤ n }. Suppose there exists constants an > 0, bn ∈ R and a nondegenrate distribution G (y) such that Then, we have almost surely, where f (x, y) denotes the bounded Lipschitz 1 function and Φ(x) is the standard normal distribution function (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
4.
M. Baroun L. Maniar G.M. NGurkata 《Nonlinear Analysis: Theory, Methods & Applications》2008,69(7):2114-2124
In this paper, we study the existence and uniqueness of almost periodic and almost automorphic solutions to the semilinear parabolic boundary differential equations where AAm|kerL generates a hyperbolic analytic semigroup on a Banach space X. The functions h and are defined on some intermediate subspaces Xβ,0<β<1, and take values in X and in a boundary space ∂X respectively. 相似文献
5.
LetS be a topological semigroup andAP(S) the space of continous complex almost periodic functions onS. We obtain characterizations of compact and weakly compact operators from a Banach spaceX into AP(S). For this we use the almost periodic compactification ofS obtained through uniform spaces. For a bounded linear operatorT fromX into AP(S), letT
5, be the translate ofT bys inS defined byT
5(x)=(Tx)
5
. We define topologies on the space of bounded linear operators fromX into AP(S) and obtain the necessary and sufficient conditions for an operatorT to be compact or weakly compact in terms of the uniform continuity of the maps→T
5. IfS is a Hausdorff topological semigroup, we also obtain characterizations of compact and weakly compact multipliers on AP(S) in terms of the uniform continuity of the map S→μs, where μs denotes the unique vector measure corresponding to the operatorT
5. 相似文献
6.
Tetiana V. Bosenko 《Central European Journal of Mathematics》2010,8(2):346-356
A linear continuous nonzero operator G: X → Y is a Daugavet center if every rank-1 operator T: X → Y satisfies ||G + T|| = ||G|| + ||T||. We study the case when either X or Y is a sum X
1⊕F
X
2 of two Banach spaces X
1 and X
2 by some two-dimensional Banach space F. We completely describe the class of those F such that for some spaces X
1 and X
2 there exists a Daugavet center acting from X
1⊕F
X
2, and the class of those F such that for some pair of spaces X
1 and X
2 there is a Daugavet center acting into X
1⊕F
X
2. We also present several examples of such Daugavet centers. 相似文献
7.
Let S be a locally compact semitopological semigroup with measure algebra M(S), M0(S) the set of all probability measures in M(S) and WF(S) the space of weakly almost periodic functionals on M(S)*. Assuming that M0(S) has the semiright invariant isometry property, it is shown that WF(S) has a topological left invariant mean (TLIM) whenever the center of M0(S) is nonempty; in particular if either the center of S is nonempty or S has a left identity, then WF(S) has a TLIM. Finally if, for each M0(S), the mapping v v * of M0(S) into itself is surjective and the center of M0(S) is nonempty, then WF(S) has a TLIM. We also generalize some results from discrete case to topological one.AMS Subject Classification (1991): 43A07 相似文献
8.
Hugo D. Junghenn 《Semigroup Forum》2003,66(2):328-336
Let $S\tilde \times T$ be a semidirect product of semitopological semigroups S and T. If S and T act on topological spaces X and Y, respectively, then under suitable conditions there is a natural action of $S\tilde \times T$ on X × Y. In this paper we characterize the almost periodic and strongly almost periodic compactification of the flow ( $S\tilde \times T$ , X × Y) in terms of related compactifications of (S, X) and (T, Y). 相似文献
9.
Let (X, ~) be a combinatorial graph the vertex set X of which is a discrete metric space. We suppose that a discrete group G acts freely on (X, ~) and that the fundamental domain with respect to the action of G contains only a finite set of points. A graph with these properties is called periodic with respect to the group G. We examine the Fredholm property and the essential spectrum of band-dominated operators acting on the spaces l
p
(X) or c_0(X), where (X, ~) is a periodic graph. Our approach is based on the thorough use of band-dominated operators. It generalizes the necessary
and sufficient results obtained in [39] in the special case and in [42] in case X = G is a general finitely generated discrete group.
Submitted: May 21, 2007. Revised: September 25, 2007. Accepted: November 5, 2007. 相似文献
10.
Alexey I. Popov 《Integral Equations and Operator Theory》2010,67(2):247-256
Given a Banach space X and a bounded linear operator T on X, a subspace Y of X is almost invariant under T if TY í Y+F{TY\subseteq Y+F} for some finite-dimensional “error” F. In this paper, we study subspaces that are almost invariant under every operator in an algebra
\mathfrak A{\mathfrak A} of operators acting on X. We show that if
\mathfrak A{\mathfrak A} is norm closed then the dimensions of “errors” corresponding to operators in
\mathfrak A{\mathfrak A} must be uniformly bounded. Also, if
\mathfrak A{\mathfrak A} is generated by a finite number of commuting operators and has an almost invariant half-space (that is, a subspace with both
infinite dimension and infinite codimension) then
\mathfrak A{\mathfrak A} has an invariant half-space. 相似文献
11.
We consider Dirichlet series zg,a(s)=?n=1¥ g(na) e-ln s{\zeta_{g,\alpha}(s)=\sum_{n=1}^\infty g(n\alpha) e^{-\lambda_n s}} for fixed irrational α and periodic functions g. We demonstrate that for Diophantine α and smooth g, the line Re(s) = 0 is a natural boundary in the Taylor series case λ
n
= n, so that the unit circle is the maximal domain of holomorphy for the almost periodic Taylor series ?n=1¥ g(na) zn{\sum_{n=1}^{\infty} g(n\alpha) z^n}. We prove that a Dirichlet series zg,a(s) = ?n=1¥ g(n a)/ns{\zeta_{g,\alpha}(s) = \sum_{n=1}^{\infty} g(n \alpha)/n^s} has an abscissa of convergence σ
0 = 0 if g is odd and real analytic and α is Diophantine. We show that if g is odd and has bounded variation and α is of bounded Diophantine type r, the abscissa of convergence σ
0 satisfies σ
0 ≤ 1 − 1/r. Using a polylogarithm expansion, we prove that if g is odd and real analytic and α is Diophantine, then the Dirichlet series ζ
g,α
(s) has an analytic continuation to the entire complex plane. 相似文献
12.
LU Chuanrong QIU Jin & XU Jianjun School of Mathematics Statistics Zhejiang University of Finance Economics Hangzhou China Department of Mathematics Zhejiang University Hangzhou China 《中国科学A辑(英文版)》2006,49(12):1788-1799
Let {Xn,-∞< n <∞} be a sequence of independent identically distributed random variables with EX1 = 0, EX12 = 1 and let Sn =∑k=1∞Xk, and Tn = Tn(X1,…,Xn) be a random function such that Tn = ASn Rn, where supn E|Rn| <∞and Rn = o(n~(1/2)) a.s., or Rn = O(n1/2-2γ) a.s., 0 <γ< 1/8. In this paper, we prove the almost sure central limit theorem (ASCLT) and the function-typed almost sure central limit theorem (FASCLT) for the random function Tn. As a consequence, it can be shown that ASCLT and FASCLT also hold for U-statistics, Von-Mises statistics, linear processes, moving average processes, error variance estimates in linear models, power sums, product-limit estimators of a continuous distribution, product-limit estimators of a quantile function, etc. 相似文献
13.
A pair of linear bounded commuting operators T1, T2 in a Banach space is said to possess a decomposition property (DePr) if
Ker (I-T1)(I-T2) = Ker (I-T1) + Ker (I-T2).
A Banach space X is said to possess a 2-decomposition property (2-DePr) if every pair of linear power bounded commuting operators in X possesses the DePr. It is known from papers of M. Laczkovich and Sz. Révész that every reflexive Banach space X has the 2-DePr.
In this paper we prove that every quasi-reflexive Banach space of order 1 has the 2-DePr but not all quasi-reflexive spaces
of order 2. We prove that a Banach space has no 2-DePr if it contains a direct sum of two non-reflexive Banach spaces. Also
we prove that if a bounded pointwise norm continuous operator group acts on X then every pair of operators belonging to it has a DePr.
A list of open problems is also included.
This revised version was published online in August 2006 with corrections to the Cover Date. 相似文献
14.
Masoud Hajarian 《Mathematical Methods in the Applied Sciences》2019,42(10):3527-3548
Analysis and design of linear periodic control systems are closely related to the periodic matrix equations. The objective of this paper is to provide four new iterative methods based on the conjugate gradient normal equation error (CGNE), conjugate gradient normal equation residual (CGNR), and least‐squares QR factorization (LSQR) algorithms to find the reflexive periodic solutions (X1,Y1,X2,Y2,…,Xσ,Yσ) of the general periodic matrix equations for i = 1,2,…,σ. The iterative methods are guaranteed to converge in a finite number of steps in the absence of round‐off errors. Finally, some numerical results are performed to illustrate the efficiency and feasibility of new methods. 相似文献
15.
David Westreich 《Israel Journal of Mathematics》1973,16(3):279-286
Using results in bifurcation theory, we show the existence of periodic solutions of a large class of non-Lagrangian systems
of the formu″+A
1
v′+B
1u+F1
(w, w′, w″)=0v″+A
2
u′+B
2v+F2
(w, w′, w″)=0 wherew=(u, v). 相似文献
16.
本文考虑 Lienard方程 x″+f (x) x′+g(x) =e(t) ,我们得到 :当 -∞ 0且 0 相似文献
17.
In this paper, we characterize the space of almost periodic (AP) functions in one variable using either a Weyl–Heisenberg (WH) system or an affine system. Our observation is that the sought-for characterization of the AP space is valid if and only if the given WH (respectively,
affine) system is an L
2(ℝ)-frame. Moreover, the frame bounds of the system are also the sharpest bounds in our characterization. This draws an intriguing
and quite unexpected connection between L
2(ℝ) representations and AP-representations.
相似文献
18.
Hermano Frid 《Bulletin of the Brazilian Mathematical Society》2001,32(1):1-35
In this paper we survey recent results on the decay of periodic and almost periodic solutions of conservation laws. We also recall some recent results on the global existence of periodic solutions of conservation laws systems which lie inBV
loc
and are constructed through Glimm scheme. The latter motivates a discussion on a possible strategy for solving the open problem of the global existence of periodic solutions of the Euler equations for nonisentropic gas dynamics. We base our decay analysis on a general result about space-time functions which are almost periodic in the space variable, established here for the first time. This result is an abstract version of Theorem 2.1 in [31], which in turn is an extention of the combined result given by Theorems 3.1–3.2 in [9]. 相似文献
19.
Yoshihiro Hamaya 《Journal of Difference Equations and Applications》2013,19(2):227-237
In order to obtain the existence of an almost periodic functional difference equation x(n + 1) = ?(n,xn ),n ∈ Z + and where xn is defined by xn (s) = x(n + s) for s ∈ Z ?, on an axiomatic phase space B, we consider a certain stability property, which is referred to as BS-stable under disturbances from Ω(?) with respect to K, this stability implies ρ-stable under disturbances from Ω(?) with respect to compact set K. 相似文献
20.
In this paper we consider a continuous mapf: X→X, whereX is a compact metric space. The existence of chaotic sets off is discussed. For the special caseX=[0,1], we prove thatf has a positive topological entropy iff it has an uncountable chaotic set in which each point is almost periodic, and iff
it has an uncountable chaotic set in which each point is chain recurrent. As an application, a uniform proof for some known
results will be given. 相似文献