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31.
We study a generalization of the classical Marcinkiewicz–Zygmund inequalities. We relate this problem to the sampling sequences in the Paley–Wiener space and by using this analogy we give sharp necessary and sufficient computable conditions for a family of points to satisfy the Marcinkiewicz–Zygmund inequalities. 相似文献
32.
J. D. Chen 《Journal of Optimization Theory and Applications》2006,131(3):383-403
The design of a robust mixed H
2/H
∞ controller for a class of uncertain neutral systems with discrete, distributed, and input time-varying delays is considered. More precisely, the proposed robust mixed H
2/H
∞ controller minimizes an upper bound of the H
2 performance measure, while guaranteeing an H
∞ norm bound constraint. Based on the Lyapunov-Krasovskii functional theory, a delay-dependent criterion is derived for the existence of a desired mixed H
2/H
∞ controller, which can be constructed easily via feasible linear matrix inequalities (LMIs). Furthermore, a convex optimization problem satisfying some LMI constraints is formulated to obtain a suboptimal robust mixed H
2/H
∞ controller achieving the minimization of an upper bound of the closed-loop H
2 performance measure. Finally, a numerical example is illustrated to show the usefulness of the obtained design method.The research reported here was supported by the National Science Council of Taiwan, ROC under Grant NSC 94-2213-E-507-002. 相似文献
33.
Mónica ClappSergio Hernández-Linares Eric Hernández-Mart?&#x;nez 《Journal of Differential Equations》2002,185(1):181-199
We consider paths of functionals starting with one which is invariant under the action of an arbitrary group of symmetries. We give conditions for the existence of an unbounded sequence of critical values of the non-symmetric functional at the end of the path in terms of the growth of the critical values of the symmetric one. We apply this to obtain a multiplicity result for a system of elliptic equations whose symmetries are perturbed by a linear term and a non-homogeneous boundary condition. 相似文献
34.
关于Banach空间中凸泛函的广义次梯度不等式 总被引:2,自引:0,他引:2
本文在前人^[1,2]的基础之上,以凸泛函的次梯度不等式为工具,将Jensen不等式推广到Banach空间中的凸泛函,导出了Banach空间中的Bochner积分型的广义Jensen不等式,给出其在Banach空间概率论中某些应用,从而推广了文献[3—6]的工作. 相似文献
35.
36.
We fix a rich probability space (,F,P). Let (H,) be a separable Hilbert space and let be the canonical cylindrical Gaussian measure on H. Given any abstract Wiener space (H,B,) over H, and for every Hilbert–Schmidt operator T: HBH which is (|{}|,)-continuous, where |{}| stands for the (Gross-measurable) norm on B, we construct an Ornstein–Uhlenbeck process : (,F,P)×[0,1](B,|{}|) as a pathwise solution of the following infinite-dimensional Langevin equation d
t
=db
t
+T(
t
)dt with the initial data 0=0, where b is a B-valued Brownian motion based on the abstract Wiener space (H,B,). The richness of the probability space (,F,P) then implies the following consequences: the probability space is independent of the abstract Wiener space (H,B,) (in the sense that (,F,P) does not depend on the choice of the Gross-measurable norm |{}|) and the space C
B
consisting of all continuous B-valued functions on [0,1] is identical with the set of all paths of . Finally, we present a way to obtain pathwise continuous solutions :d
t
=
db
t
+
t
dt
with initial data 0=0, where ,R,0 and 0<. 相似文献
37.
Lu Chuanrong Zhejiang University of Finance Economics Zhejiang University Hangzhou China. 《高校应用数学学报(英文版)》2005,20(3):331-337
§1Introductionandresults A2-parameterGaussianprocess{Z(t,s);t,s≥0}iacalleda2-parameterfractional Wienerprocesswithorderα(0<α<1),ifZ(0,0)=0a.s.EZ(s,t)=0anditscovariance EZ(t1,s1)Z(t2,s2)={|t1|2α+|t2|2α-|t2-t1|2α}{|s1|2α+|s2|2α-|s2-s1|2α}/4.LetR=[x1,x2]×[y1,y2],DT={(x,y)∶0≤x,y≤bT,xy≤T}.Let0相似文献
38.
Steffen Roch 《Numerical Functional Analysis & Optimization》2013,34(1-2):241-253
The paper deals with spectral approximation of Wiener-Hopf operators acting on Lp -spaces by their finite sections. The generating functions of the Wiener-Hopf operators are supposed to be continuous plus almost periodic.While the usual spectra of the finite sections drastically fail to converge to the spectrum of the Wiener-Hopf operator,it turns out that other spectral approximants, viz. the pseudospectra and the numerical ranges, do converge perfectly.The proof requires a modified approach to the finite section method for Wiener-Hopf operators. This note generalizes results obtained by Böttcher, Grudsky and Silbermann for the case of continuous generating functions. 相似文献
39.
Let G be a connected graph and η(G)=Sz(G)−W(G), where W(G) and Sz(G) are the Wiener and Szeged indices of G, respectively. A well-known result of Klav?ar, Rajapakse, and Gutman states that η(G)≥0, and by a result of Dobrynin and Gutman η(G)=0 if and only if each block of G is complete. In this paper, a path-edge matrix for the graph G is presented by which it is possible to classify the graphs in which η(G)=2. It is also proved that there is no graph G with the property that η(G)=1 or η(G)=3. Finally, it is proved that, for a given positive integer k,k≠1,3, there exists a graph G with η(G)=k. 相似文献
40.
可以接轨道得到带白噪声的随机耗散Camassa-Holm方程的唯—解并且可以检验该解产生随机动力系统,从而证明了该随机动力系统在H02中存在紧的随机吸引子. 相似文献