共查询到18条相似文献,搜索用时 93 毫秒
1.
本文利用广义双正交序列研究广义Riesz基的等价刻画,得到了算子序列是广义Riesz基当且仅当该算子列是广义完备的广义Bessel序列,且它存在广义双正交序列及这个双正交序列也是广义完备的广义Bessel序列.进一步证明了等价刻画中两个广义Bessel序列的广义完备性条件可以去掉一个(或者任一个),并举例说明了广义双正交,广义完备与广义Bessel条件之间的关系. 相似文献
2.
广义正交基是Hilbert 空间中正交基的一个自然推广. 本文首先给出一个广义正交基存在的较弱的充要条件; 然后研究广义正交基的性质, 特别地, 得到广义正交基版本的一些有关正交基的经典性质, 如广义正交基的Bessel 等式和不等式等. 作为广义正交基的一个应用, 本文给出广义Riesz 基的一些新刻画. 最后本文讨论广义框架的冗余问题. 相似文献
3.
《数学的实践与认识》2019,(21)
研究广义完全Bessel序列和广义下半框架,包括离散和连续两种情形.首先讨论广义完全Bessel序列的分析算子性质;其次建立广义下半框架的充要条件;最后证明广义完全Bessel序列的对偶是广义下半框架. 相似文献
4.
Banach空间中的X_d框架与Reisz基 总被引:1,自引:0,他引:1
本文引入并研究了Banach空间中的X_d框架,X_d Bessel列,紧X_d框架,独立X_d框架和X_d Riesz基等概念,给出了X_d框架和独立X_d框架的算子等价刻画,Banach空间X中存在X_d框架或X_d Riesz基的充要条件以及X_d框架的对偶框架存在的充要条件,讨论了Banach空间的基和X_d框架,X_d Riesz基之间的关系. 相似文献
5.
本文说明Banach空间上p-fusion框架和p-框架有紧密联系.应用分析算子和合成算子给出p-fusion Bessel序列、p-fusion框架和q-fusion Riesz基的等价描述. 相似文献
6.
董芳芳 《应用泛函分析学报》2020,(3):175-181
本文引入了Hilbert K-模上的广义框架,广义框架变换和正交投影等概念,研究了广义标准正交基,广义(正规)紧框架(广义Bessel序列)的分解,得到了广义框架变换和正交投影之间的关系. 相似文献
7.
Hilbert空间算子T∈B(H)称为是一致可逆的,若对任意的S∈B(H),TS与ST的可逆性相同.本文中根据一致可逆性质定义了一个新的谱集,用该谱集来研究广义(ω)性质的稳定性,即考虑了Hilbert空间上有界线性算子的有限秩摄动、幂零摄动以及Riesz摄动的广义(ω)性质.之后研究了能分解成有限个正规算子乘积的一类算子的广义(ω)性质的稳定性. 相似文献
8.
9.
10.
研究一般Hilbert空间X上的闭环系统广义本征元的Riesz基生成问题,采用基扰动的方法,给出了闭环系统广义本征元生成Riesz基的充分条件,并用实例说明了结论的应用. 相似文献
11.
Chun-Yan Li 《Complex Analysis and Operator Theory》2012,6(1):1-21
In this paper, operator Bessel sequences, operator frames, Banach operator frames, Operator Riesz bases for Banach spaces
and dual frames of an operator frame are introduced and discussed. The necessary and sufficient condition for a Banach space
to have an operator frame, a Banach operator frame or an operator Riesz basis are given. In addition, operator frames and
operator Riesz bases are characterized by the analysis operator of operator Bessel sequences. 相似文献
12.
G-frames and g-Riesz bases 总被引:2,自引:0,他引:2
Wenchang Sun 《Journal of Mathematical Analysis and Applications》2006,322(1):437-452
G-frames are generalized frames which include ordinary frames, bounded invertible linear operators, as well as many recent generalizations of frames, e.g., bounded quasi-projectors and frames of subspaces. G-frames are natural generalizations of frames and provide more choices on analyzing functions from frame expansion coefficients. We give characterizations of g-frames and prove that g-frames share many useful properties with frames. We also give a generalized version of Riesz bases and orthonormal bases. As an application, we get atomic resolutions for bounded linear operators. 相似文献
13.
The objective of this paper is to investigate the question of modifying a given generalized Bessel sequence to yield a generalized frame or a tight generalized frame by finite extension. Some necessary and sufficient conditions for the finite extensions of generalized Bessel sequences to generalized frames or tight generalized frames are provided, and every result is illustrated by the corresponding example. 相似文献
14.
We introduce generalized Bessel and Riesz potentials on metric measure spaces and the corresponding potential spaces. Estimates
of the Bessel and Riesz kernels are given which reflect the intrinsic structure of the spaces. Finally, we state the relationship
between Bessel (or Riesz) operators and subordinate semigroups.
相似文献
15.
This paper addresses the theory of multi-window subspace Gabor frame with rational time-frequency parameter products.With the help of a suitable Zak transform matrix,we characterize multi-window subspace Gabor frames,Riesz bases,orthonormal bases and the uniqueness of Gabor duals of type I and type II.Using these characterizations we obtain a class of multi-window subspace Gabor frames,Riesz bases,orthonormal bases,and at the same time we derive an explicit expression of their Gabor duals of type I and type II.As an application of the above results,we obtain characterizations of multi-window Gabor frames,Riesz bases and orthonormal bases for L2(R),and derive a parametric expression of Gabor duals for multi-window Gabor frames in L2(R). 相似文献
16.
Exact g-frames in Hilbert spaces 总被引:2,自引:0,他引:2
Jian-Zhen Li 《Journal of Mathematical Analysis and Applications》2011,374(1):201-209
G-frames, which were considered recently as generalized frames in Hilbert spaces, have many properties similar to those of frames, but not all the properties are similar. For example, exact frames are equivalent to Riesz bases, but exact g-frames are not equivalent to g-Riesz bases. In this paper, we firstly give a characterization of an exact g-frame in a complex Hilbert space. We also obtain an equivalent relation between an exact g-frame and a g-Riesz basis under some conditions. Lastly we consider the stability of an exact g-frame for a Hilbert space under perturbation. These properties of exact g-frames for Hilbert spaces are not similar to those of exact frames. 相似文献
17.
In this paper, we define the generalized Gauss Weierstrass semigroups with Weierstrass kernel, and give some of their properties. Using them, we study the inversion formulas for the generalized Riesz and Bessel potentials, generated by the generalized shift operators and associated with the Laplace Bessel differential operator. 相似文献
18.
四元数Hilbert空间在应用物理科学特别是量子物理中占有重要地位.本文讨论四元数Hilbert空间的框架理论, 在四元数Hilbert空间中引入了Riesz基的概念, 在此基础上刻画了Riesz基,给出了它们的一些等价条件; 特别地, 得到了四元数Hilbert空间中的一个序列是Riesz基的充要条件是它是一个具有双正交序列的完备Bessel序列,且它的双正交序列也是一个完备Bessel序列; 并进一步证明了双正交序列中一个序列的完备性可以从特征刻画中去除.文中举例说明了双正交性、完备性和Bessel性质之间的关系. 相似文献