| Hilbert空间中连续广义框架的分解 |
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| 引用本文： | 张伟,付艳玲. Hilbert空间中连续广义框架的分解[J]. 山东大学学报(理学版), 2019, 54(8): 76-80. DOI: 10.6040/j.issn.1671-9352.0.2018.724 |
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| 作者姓名： | 张伟 付艳玲 |
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| 作者单位： | 1.河南财经政法大学数学与信息科学学院, 河南 郑州 450046;2.河南财政金融学院信息工程系, 河南 郑州 451464 |
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| 基金项目： | 国家自然科学基金资助项目(11761079);河南省自然科学基金资助项目(152300410207) |
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| 摘 要： | 利用连续广义预框架算子,刻画了连续广义框架、Parseval连续广义框架、连续广义Riesz基及连续广义标准正交基;通过已建立的刻画结果及有界算子的分解,得到了连续广义框架可以表示特殊的或者更简单的连续广义框架的线性组合,比如连续广义标准正交基、连续广义Riesz-基、Parseval连续广义框架。
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| 关 键 词： | 广义框架 连续广义框架 连续广义标准正交基 算子 |
On decompositions of continuous generalized frames in Hilbert spaces |
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| ZHANG Wei,FU Yan-ling. On decompositions of continuous generalized frames in Hilbert spaces[J]. Journal of Shandong University, 2019, 54(8): 76-80. DOI: 10.6040/j.issn.1671-9352.0.2018.724 |
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| Authors: | ZHANG Wei FU Yan-ling |
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| Affiliation: | 1. School of Mathematics and Information Sciences, Henan University of Economics and Law, Zhengzhou 450046, Henan, China;2. Department of Information Engineering, Henan Finance University, Zhengzhou 451464, Henan, China |
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| Abstract: | This paper establishes the characterization of continuous generalized frames,Parseval continuous g-frames,continuous generalized Riesz bases and continuous generalized orthonormal bases in term of the continuous generalized preframe operator. Using the established characterization results and decompositions of bounded operators, the representation of continuous generalized frames in term of linear combinations of simpler ones such as continuous generalized orthonormal bases, continuous generalized Riesz bases and Parseval continuous generalized frames is studied. |
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| Keywords: | generalized frame continuous generalized frame continuous generalized orthonormal base operator |
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