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学者姓名:李云章
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摘要 :
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空间的标架理论,引入了四元数Hilbert空间中近似对偶标架的概念,刻画了(近似)对偶标架,给出了由一个(近似)对偶标架对构造其它(近似)对偶标架对的一些充分条件,得到了(近似)对偶标架稳定性的若干结果.
关键词 :
对偶标架 对偶标架 近似对偶标架 近似对偶标架 四元数Hilbert空间 四元数Hilbert空间
引用:
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GB/T 7714 | 张伟 , 李云章 . 四元数Hilbert空间中近似对偶与对偶标架 [J]. | 数学学报 , 2021 , 64 (4) : 613-626 . |
MLA | 张伟 等. "四元数Hilbert空间中近似对偶与对偶标架" . | 数学学报 64 . 4 (2021) : 613-626 . |
APA | 张伟 , 李云章 . 四元数Hilbert空间中近似对偶与对偶标架 . | 数学学报 , 2021 , 64 (4) , 613-626 . |
导入链接 | NoteExpress RIS BibTex |
摘要 :
Structured frames in L-2(R), such as wavelet and Gabor frames, have been extensively studied. But the analysis on L-2(R+) with R+ = (0, infinity) has been rarely reported. It is because R is a group under addition but R+ is not. This results in L-2(R+) admitting no traditional wavelet or Gabor frames. Recently, the concept of F-a-frame in L-2(R+) was introduced and studied. In this paper, we present some identities and inequalities for F-a-frame sequences in L-2(R+).
关键词 :
Frame Frame F-a-frame F-a-frame Parseval frame sequence Parseval frame sequence Frame sequence Frame sequence F-a-frame sequence F-a-frame sequence Parseval F-a-frame sequence Parseval F-a-frame sequence
引用:
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GB/T 7714 | Li, Yun-Zhang , Wang, Bo-Yang . Some Identities and Inequalities for F-a-Frame Sequences in L-2(R+) [J]. | BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY , 2021 . |
MLA | Li, Yun-Zhang 等. "Some Identities and Inequalities for F-a-Frame Sequences in L-2(R+)" . | BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY (2021) . |
APA | Li, Yun-Zhang , Wang, Bo-Yang . Some Identities and Inequalities for F-a-Frame Sequences in L-2(R+) . | BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY , 2021 . |
导入链接 | NoteExpress RIS BibTex |
摘要 :
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空间的标架理论,引入了四元数Hilbert空间中近似对偶标架的概念,刻画了(近似)对偶标架,给出了由一个(近似)对偶标架对构造其它(近似)对偶标架对的一些充分条件,得到了(近似)对偶标架稳定性的若干结果.
关键词 :
对偶标架 对偶标架 近似对偶标架 近似对偶标架 四元数Hilbert空间 四元数Hilbert空间
引用:
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GB/T 7714 | 张伟 , 李云章 . 四元数Hilbert空间中近似对偶与对偶标架 [J]. | 数学学报(中文版) , 2021 , 64 (04) : 613-626 . |
MLA | 张伟 等. "四元数Hilbert空间中近似对偶与对偶标架" . | 数学学报(中文版) 64 . 04 (2021) : 613-626 . |
APA | 张伟 , 李云章 . 四元数Hilbert空间中近似对偶与对偶标架 . | 数学学报(中文版) , 2021 , 64 (04) , 613-626 . |
导入链接 | NoteExpress RIS BibTex |
摘要 :
控制框架是框架概念的推广,在复杂线性系统求解中具有重要的应用.本文讨论控制连续g-框架理论:首先,利用算子方法,建立了控制连续g-框架与连续g-框架的联系,得到了其诱导刻画;也从一个给定的控制连续g-框架构造出新的控制连续g-框架.其次,给出了控制连续g-框架新的恒等分解.最后,研究了控制连续g-框扰动的稳定性.
关键词 :
连续g-框架 连续g-框架 稳定性 稳定性 控制连续g-框架 控制连续g-框架 框架 框架
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GB/T 7714 | 张伟 , 李云章 . Hilbert空间中控制连续g-框架 [J]. | 数学学报(中文版) , 2021 , 64 (03) : 515-528 . |
MLA | 张伟 等. "Hilbert空间中控制连续g-框架" . | 数学学报(中文版) 64 . 03 (2021) : 515-528 . |
APA | 张伟 , 李云章 . Hilbert空间中控制连续g-框架 . | 数学学报(中文版) , 2021 , 64 (03) , 515-528 . |
导入链接 | NoteExpress RIS BibTex |
摘要 :
Hilbert空间中控制连续g-框架
关键词 :
框架 框架 稳定性 稳定性 控制连续g-框架 控制连续g-框架 连续g-框架 连续g-框架
引用:
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GB/T 7714 | 张伟 , 李云章 , 数学学报:中文版 . Hilbert空间中控制连续g-框架 [J]. | 张伟 , 2021 , 64 (3) : 515-528 . |
MLA | 张伟 等. "Hilbert空间中控制连续g-框架" . | 张伟 64 . 3 (2021) : 515-528 . |
APA | 张伟 , 李云章 , 数学学报:中文版 . Hilbert空间中控制连续g-框架 . | 张伟 , 2021 , 64 (3) , 515-528 . |
导入链接 | NoteExpress RIS BibTex |
摘要 :
控制框架是框架概念的推广,在复杂线性系统求解中具有重要的应用.本文讨论控制连续g-框架理论:首先,利用算子方法,建立了控制连续g-框架与连续g-框架的联系,得到了其诱导刻画;也从一个给定的控制连续g-框架构造出新的控制连续g-框架.其次,给出了控制连续g-框架新的恒等分解.最后,研究了控制连续g-框扰动的稳定性.
引用:
复制并粘贴一种已设定好的引用格式,或利用其中一个链接导入到文献管理软件中。
GB/T 7714 | 张伟 , 李云章 . Hilbert空间中控制连续g-框架 [J]. | 数学学报 , 2021 , 64 (3) : 515-528 . |
MLA | 张伟 等. "Hilbert空间中控制连续g-框架" . | 数学学报 64 . 3 (2021) : 515-528 . |
APA | 张伟 , 李云章 . Hilbert空间中控制连续g-框架 . | 数学学报 , 2021 , 64 (3) , 515-528 . |
导入链接 | NoteExpress RIS BibTex |
摘要 :
The concept of Hilbert-Schmidt frame (HS-frame) was first introduced by Sadeghi and Arefijamaal in 2012. It is more general than g-frames, and thus, covers many generalizations of frames. This paper addresses the theory of HS-frames. We present a parametric and algebraic formula for all duals of an arbitrarily given HS-frame; prove that the canonical HS-dual induces a minimal-norm expression of the elements in Hilbert spaces; characterize when an HS-frame is an HS- Riesz basis, and when an HS-Bessel sequence is an HS-Riesz sequence (HS-Riesz basis) in terms of Gram matrices.
关键词 :
dual Hilbert-Schmidt frames dual Hilbert-Schmidt frames Frame Frame Hilbert-Schmidt Bessel sequence Hilbert-Schmidt Bessel sequence Hilbert-Schmidt frame Hilbert-Schmidt frame Hilbert-Schmidt Riesz basis Hilbert-Schmidt Riesz basis
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GB/T 7714 | Li, Ya-Nan , Li, Yun-Zhang . Hilbert-Schmidt frames and their duals [J]. | INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING , 2021 , 19 (05) . |
MLA | Li, Ya-Nan 等. "Hilbert-Schmidt frames and their duals" . | INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING 19 . 05 (2021) . |
APA | Li, Ya-Nan , Li, Yun-Zhang . Hilbert-Schmidt frames and their duals . | INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING , 2021 , 19 (05) . |
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摘要 :
Let K be a bounded linear operator on a separable Hilbert space H. Gvrua in 2012 proposed the notion of K-frame. It is exactly an atomic system with respect to K, and allows a stable reconstruction in range(K). This paper addresses the construction of K-frames. We characterize bounded linear operators on l2 that transform a pair of Bessel sequences into a K-frame; present a sufficient condition to obtain K-frames from two orthogonal (disjoint) K-frames. Moreover, when dim(H) © 2021 Elsevier Inc.
关键词 :
Mathematical operators Mathematical operators Mathematical transformations Mathematical transformations
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GB/T 7714 | Li, Yun-Zhang , Li, Ya-Nan . Constructing more K-frames [J]. | Linear Algebra and Its Applications , 2021 , 616 : 45-65 . |
MLA | Li, Yun-Zhang 等. "Constructing more K-frames" . | Linear Algebra and Its Applications 616 (2021) : 45-65 . |
APA | Li, Yun-Zhang , Li, Ya-Nan . Constructing more K-frames . | Linear Algebra and Its Applications , 2021 , 616 , 45-65 . |
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摘要 :
The atomic decomposition of signals is one of the most important problems in the frame theory. K-dual frame pairs may be used to stably reconstruct elements from the range of bounded linear operators on Hilbert spaces. The purpose of this paper is making K-dual frame pairs and finding common K-dual Bessel sequence. We present a sufficient condition on operators on (Formula presented.) which takes a K-dual frame pairs to other ones; characterize bounded linear operators on (Formula presented.) that transform K-dual frame pairs to other ones; prove that two Bessel sequences can always be extended to a K-dual frame pair, and that two orthogonal K-frames have a common K-dual Bessel sequence under certain conditions; and obtain a sufficient condition which the K-duals of one K-frame is contained in the ones of another K-frames. Abundant examples are also provided to illustrate the generality of the theory. © 2021 Taylor & Francis Group, LLC.
关键词 :
Mathematical operators Mathematical operators Signal processing Signal processing
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GB/T 7714 | Li, Ya-Nan , Li, Yun-Zhang . Making and Sharing K-Dual Frame Pairs [J]. | Numerical Functional Analysis and Optimization , 2021 , 42 (2) : 155-179 . |
MLA | Li, Ya-Nan 等. "Making and Sharing K-Dual Frame Pairs" . | Numerical Functional Analysis and Optimization 42 . 2 (2021) : 155-179 . |
APA | Li, Ya-Nan , Li, Yun-Zhang . Making and Sharing K-Dual Frame Pairs . | Numerical Functional Analysis and Optimization , 2021 , 42 (2) , 155-179 . |
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摘要 :
Recently, duality principles in g-frame theory were studied. This paper addresses a relaxation of g-R-duals. We introduce the notion of weak g-R-dual in g-frame theory setting, and present the link between frame properties of a bounded operator sequence and its weak g-R-duals. Using weak g-R-duals, we characterize g-frames and (unitary) equivalence between g-frames. And using pseudo-inverse operators, we represent the canonical duals of weak g-R-duals. Some examples are also provided.
关键词 :
duality principle duality principle Frame Frame g-frame g-frame g-R-dual g-R-dual weak g-R-dual weak g-R-dual
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GB/T 7714 | Li, Yun-Zhang , Dong, Jian . Duality relations associated with weak g-R-duals [J]. | LINEAR & MULTILINEAR ALGEBRA , 2021 . |
MLA | Li, Yun-Zhang 等. "Duality relations associated with weak g-R-duals" . | LINEAR & MULTILINEAR ALGEBRA (2021) . |
APA | Li, Yun-Zhang , Dong, Jian . Duality relations associated with weak g-R-duals . | LINEAR & MULTILINEAR ALGEBRA , 2021 . |
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