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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：
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 , 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 notion of R-dual in general Hilbert spaces was first introduced by Casazza et al. (J Fourier Anal Appl 10:383-408, 2004), with the motivation to obtain a general version of the duality principle in Gabor analysis. On the other hand, the space L-2(R+) of square integrable functions on the half real line R+ admits no traditional wavelet or Gabor frame due to R+ being not a group under addition. Fa-frame theory based on "function-valued inner product" is a new tool for analysis on L-2(R+). This paper addresses duality relations for Fa-frame theory in L-2(R+). We introduce the notion of Fa-R-dual of a given sequence in L-2(R+), and obtain some duality principles. Specifically, we prove that a sequence in L-2(R+) is an F-a-frame (F-a-Bessel sequence, F-a-Riesz basis, F-a-frame sequence) if and only if its F-a-R-dual is an FaRiesz sequence (F-a-Bessel sequence, F-a-Riesz basis, Fa-frame sequence), and that two sequences in L-2(R+) form a pair of Fa-dual frames if and only if their Fa-R-duals are F-a-biorthonormal.
关键词 ：
F-a-frame F-a-frame F-a-R-dual F-a-R-dual F-a-Riesz sequence F-a-Riesz sequence Frame Frame R-dual R-dual
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| GB/T 7714 | Li, Yun-Zhang , Hussain, Tufail . Duality Principles for F-a-Frame Theory in L-2(R+) [J]. | BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY , 2021 , 44 (4) : 2401-2423 . |
| MLA | Li, Yun-Zhang 等. "Duality Principles for F-a-Frame Theory in L-2(R+)" . | BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY 44 . 4 (2021) : 2401-2423 . |
| APA | Li, Yun-Zhang , Hussain, Tufail . Duality Principles for F-a-Frame Theory in L-2(R+) . | BULLETIN OF THE MALAYSIAN MATHEMATICAL SCIENCES SOCIETY , 2021 , 44 (4) , 2401-2423 . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
Since the introduction of R-duals by Casazza, Kutyniok and Lammers with the motivation to obtain a general version of duality principle in Gabor analysis, various R-duals and some relaxations of the R-dual setup have been introduced and studied by some mathematicians. They provide a powerful tool in the analysis of duality relations in general frame theory, and are far beyond the duality principle in Gabor analysis. In this paper, we introduce the concept of generalized weak R-dual based on a pair of frames which is a relaxation of the R-dual setup. Using generalized weak R-duals, we characterize the frame properties of a sequence and the equivalence between two frames, prove that the generalized weak R-duals of frames (Riesz bases) are frame sequences (frames), and present a coefficient expression corresponding to the canonical duals of generalized weak R-duals. Some examples are provided to illustrate the generality of the theory.
关键词 ：
duality principle duality principle Frame Frame generalized weak R-dual generalized weak R-dual R-dual R-dual weak R-dual weak R-dual
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| GB/T 7714 | Dong, Jian , Li, Yun-Zhang . Duality relations for a class of generalized weak R-duals [J]. | INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING , 2021 , 19 (03) . |
| MLA | Dong, Jian 等. "Duality relations for a class of generalized weak R-duals" . | INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING 19 . 03 (2021) . |
| APA | Dong, Jian , Li, Yun-Zhang . Duality relations for a class of generalized weak R-duals . | INTERNATIONAL JOURNAL OF WAVELETS MULTIRESOLUTION AND INFORMATION PROCESSING , 2021 , 19 (03) . |
| 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 Hilbert-Schmidt Bessel sequence Hilbert-Schmidt Bessel sequence Hilbert-Schmidt Riesz basis Hilbert-Schmidt Riesz basis Frame Frame Hilbert-Schmidt frame Hilbert-Schmidt frame
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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) . |
| 导入链接 | NoteExpress RIS BibTex |
摘要 ：
This paper addresses duality relations in HS-frame theory. By introducing the notion of HS-R-dual sequence, some duality relations and related results are obtained. We prove that a sequence is an HS-frame (HS-frame sequence, HS-Riesz basis) if and only if its HS-R-dual sequence is an HS-Riesz sequence (HS-frame sequence, HS-Riesz basis) and characterize the (unitary) equivalence between two HS-frames in terms of their HS-R-duals and transition matrices, respectively. We characterize HS-R-duals and prove that, given an HS-frame, among all its dual HS-frames, only the canonical dual admits minimal-norm HS-R-dual. And using HS-R-duals, we also characterize dual HS-frame pairs. © 2020 John Wiley & Sons, Ltd.
关键词 ：
Mathematical techniques Mathematical techniques Engineering Engineering
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| GB/T 7714 | Dong, Jian , Li, Yun-Zhang . Duality principles in Hilbert-Schmidt frame theory [J]. | Mathematical Methods in the Applied Sciences , 2021 , 44 (6) : 4888-4906 . |
| MLA | Dong, Jian 等. "Duality principles in Hilbert-Schmidt frame theory" . | Mathematical Methods in the Applied Sciences 44 . 6 (2021) : 4888-4906 . |
| APA | Dong, Jian , Li, Yun-Zhang . Duality principles in Hilbert-Schmidt frame theory . | Mathematical Methods in the Applied Sciences , 2021 , 44 (6) , 4888-4906 . |
| 导入链接 | NoteExpress RIS BibTex |
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