K-g-框架与子空间对偶g-框架

在Hilbert空间中定义K-g-框架,探讨K-g-框架与g-框架的一些本质差别.利用特殊闭子空间的对偶g-框架来刻画K-g-框架,给出构造特殊闭子空间对偶g-框架的一种方法,并介绍相关的K-g-框架的一些性质.     

Hilbert空间中K-g-框架的一些新结果

利用算子理论方法构建了Hilbert空间中K-g-框架的一个新对偶,通过它等价刻画了关于不同闭子空间序列的K-g-框架和g-Bessel序列之间的关系.特别地,利用对偶K-g-框架得到了K-g框架稳定性的新结果.此外给出了构造K-g-框架的一些新方法.     

Orlicz序列空间的对偶映射

本文研究Orlicz序列空间的对偶映射,给出对偶映象集为弱紧集的充分必要 条件.作为推论,得到Orlicz序列空间的弱接近光滑性的充要条件.     

Hilbert空间中的g-Bessel序列的一些等式与不等式(II)

Hilbert 空间中的g- 框架是框架的自然推广, 它们包含了许多推广的框架, 如子空间框架或fusion 框架、斜框架和拟框架等. 它们有许多与框架类似的性质, 但是并不是所有的性质都是相似的.例如, 无冗框架等价于Riesz 基, 但是无冗g- 框架不等价于g-Riesz 基. 一些作者将Hilbert 空间中的框架和对偶框架的等式和不等式推广到g- 框架和对偶g- 框架. 本文建立Hilbert 空间中的g-Bessel序列或g- 框架的一些新的等式和不等式. 本文还给出这些不等式的等号成立的充要条件. 这些结果推广和改进了由Balan, Casazza 和G?vruta 等得到的著名结果.     

Hilbert空间中的K-g-框架的性质

在复Hilbert空间中定义了K-g-框架与K-g-Riesz基,探讨K-g-框架与g-框架的一些性质差别,并给出了K-g-Riesz基的等价刻画.利用分析与框架理论上的方法和技巧,研究了复Hilbert空间中K-g-框架与K-g-Riesz基扰动的稳定性,得到了K-g-框架与K-g-Riesz基满足扰动稳定性的充分条件.     

由多重贝塞尔序列扩充为仿射框架

仿射框架在信号处理中有实用性.运用算子理论与时频分析,将两个二重贝塞尔序列扩充为一对对偶二重仿射框架.再由已知的一对多重贝塞尔序列添加若干个函数使它们扩充为一对对偶多重仿射框架,得到了多重Gabor框架的特征不等式.     

对偶框架稀疏性的两个结果

利用矩阵Φ的概念sparkj(Φ)讨论对偶框架的稀疏性.首先,建立谱块算法框架的最佳稀疏对偶框架的稀疏值之新表示形式;其次,给出对偶框架稀疏值为最小的有限框架的充要条件.     

Hilbert空间中的斜对偶g-框架

在Hilbert空间中把斜对偶原理推广到更一般的g-框架.我们给出了{A_j:j∈J}是g-框架{F_j:j∈J}的一个斜对偶g-框架的等价条件,还给出了一个斜对偶g-框架对是对称的充分条件.最后,在不同的条件下构造了几对斜对偶g-框架.     

K-g-框架的稳定性与不等式

K-g-框架是将算子K引入到g-框架中的一种特殊框架.采用泛函分析中的技巧和方法,研究K-g-框架的稳定性,并得到了四个K-g-框架在扰动情况下稳定的充分条件.此外,结合算子K和框架算子S衍生出K-g-框架的三个等式,并通过引入参数λ建立关于K-g-框架的一些不等式.     

Fock空间上的对偶Toeplitz代数

通过符号映射研究Fock空间之正交补空间上对偶Toeplitz代数的结构,得到了Fock空间上对偶Toeplitz代数的一个短正合序列.并研究了对偶Toeplitz算子谱的性质.     

Bessel sequences,wavelet frames,duals and extensions

From the perspectives of duality and extensions, Gabor frames and wavelet frames have contrasting behaviour. Our chief concern here is about duality. Canonical duals of wavelet frames may not be wavelet frames, whereas canonical duals of Gabor frames are Gabor frames. Keeping these in view, we give several constructions of wavelet frames with wavelet canonical duals. For this, a simple characterisation of Bessel sequences and a general commutativity result are given, the former also leading naturally to some extension results.     

Some New Results on the Chu Duality of Discrete Groups

This paper deals mainly with the Chu duality of discrete groups. Among other results, we give sufficient conditions for an FC group to satisfy Chu duality and characterize when the Chu quasi-dual and the Takahashi quasi-dual of a group G coincide. As a consequence, it follows that when G is a weak sum of a family of finite simple groups, if the exponent of the groups in the family is bounded then G satisfies Chu duality; on the other hand, if the exponent of the group goes to infinity, then the Chu quasi-dual of G coincides with its Takahashi quasi-dual. We also present examples of discrete groups whose Chu quasi-duals are not locally compact and examples of discrete Chu reflexive groups which contain non-trivial sequences converging in the Bohr topology of the groups. Our results systematize some previous work and answer some open questions on the subject [2, 16, 3].     

Stable and Total Fenchel Duality for Composed Convex Optimization Problems

In this paper, we consider the composed convex optimization problem which consists in minimizing the sum of a convex function and a convex composite function. By using the properties of the epigraph of the conjugate functions and the subdifferentials of convex functions, we give some new constraint qualifications which completely characterize the strong Fenchel duality and the total Fenchel duality for composed convex optimiztion problem in real locally convex Hausdorff topological vector spaces.     

Some New Results on the Chu Duality of Discrete Groups

This paper deals mainly with the Chu duality of discrete groups. Among other results, we give sufficient conditions for an FC group to satisfy Chu duality and characterize when the Chu quasi-dual and the Takahashi quasi-dual of a group G coincide. As a consequence, it follows that when G is a weak sum of a family of finite simple groups, if the exponent of the groups in the family is bounded then G satisfies Chu duality; on the other hand, if the exponent of the group goes to infinity, then the Chu quasi-dual of G coincides with its Takahashi quasi-dual. We also present examples of discrete groups whose Chu quasi-duals are not locally compact and examples of discrete Chu reflexive groups which contain non-trivial sequences converging in the Bohr topology of the groups. Our results systematize some previous work and answer some open questions on the subject [2, 16, 3]. The first named author acknowledges partial financial support by the Spanish Ministry of Science (including FEDER funds), grant MTM2004-07665-C02-01; and the Generalitat Valenciana, grant GV04B-019.     

求解约束规划的一个非线性Lagrange函数

本文提出了一个求解不等式约束优化问题的非线性Lagrange函数,并构造了基于该函数的对偶算法.证明了当参数σ小于某一阈值σ_0时,由算法生成的原始-对偶点列是局部收敛的,并给出了原始-对偶解的误差估计.此外,建立了基于该函数的对偶理论.最后给出了算法的数值结果.     

Nonlinear BVPS with functional parameters

We study the existence, nonexistence and properties of solutions for a certain class of second-order ODEs and their dependence on functional parameters, also in the case when nonlinearities are, in some sense, singular. This approach is based on variational methods and cover both sublinear and superlinear cases. We develop a duality theory and variational principles for this problem. As a consequence of the duality theory we give a numerical version of the variational principle which enables approximation of the solution for our problem. We apply these results to obtain the existence of bounded, radial and positive classical solutions for the BVP of elliptic type. Observe that our method allows us to investigate a certain class of elliptic systems in both bounded annular domain and exterior domain.     

On sum and stability of g-frames in Hilbert spaces

In this paper, we give some new results on sum and stability of g-frames in Hilbert spaces. Since the finite sum of g-frames may not be a g-frame for the Hilbert space, we give a necessary and sufficient condition and some sufficient conditions for the finite sum of g-frames to be a g-frame. We also show that every g-sequence in Hilbert space can be expanded to a tight g-frame by adding a linear bounded operator. Moreover, we obtain some sufficient conditions under which g-frames (and the finite sum of g-frames) are stable under small perturbations.     

On duality theory in multiobjective programming

In this paper, we study different vector-valued Lagrangian functions and we develop a duality theory based upon these functions for nonlinear multiobjective programming problems. The saddle-point theorem and the duality theorem are derived for these problems under appropriate convexity assumptions. We also give some relationships between multiobjective optimizations and scalarized problems. A duality theory obtained by using the concept of vector-valued conjugate functions is discussed.The author is grateful to the reviewer for many valuable comments and helpful suggestions.     

凸规划的一个对偶问题

1引言考虑标准的非可微凸规划问题