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| Basic Results of Gabor Frame on Local Fields | |
| 引用本文： | Dengfeng LI,Huikun JIANG. Basic Results of Gabor Frame on Local Fields[J]. 数学年刊B辑(英文版), 2007, 28(2): 165-176. DOI: 10.1007/s11401-005-0389-0 |
| 作者姓名： | Dengfeng LI Huikun JIANG |
| 作者单位： | Dengfeng LI Huikun JIANG Institute of Applied Mathematics，College of Mathematics and Information Science，Henan University，Kaifeng 475001，Henan，China. Department of Mathematics，Nanjing University，Nanjing 210093，China. |
| 基金项目： | 国家自然科学基金;中国博士后科学基金;河南省教育厅资助项目 |
| 摘 要： | Basic facts for Gabor frame {Eu(m)bTu(n)ag}m,n∈p on local field are investigated. Accurately, that the canonical dual of frame {Eu(m)bTu(n)ag}m,n∈p also has the Gabor structure is showed; that the product ab decides whether it is possible for {Eu(m)bTu(n)ag}m,n∈p to be a frame for L2(K) is discussed; some necessary conditions and two sufficient conditions of Gabor frame for L2(K) are established. An example is finally given. |
| 关 键 词： | Gabor标架 局部域 希尔伯特空间 典范对偶性 |
| 收稿时间： | 2005-09-13 |
| 修稿时间： | 2014-06-06 |
Basic Results of Gabor Frame on Local Fields |
|
| Dengfeng LI and Huikun JIANG. Basic Results of Gabor Frame on Local Fields[J]. Chinese Annals of Mathematics,Series B, 2007, 28(2): 165-176. DOI: 10.1007/s11401-005-0389-0 | |
| Authors: | Dengfeng LI and Huikun JIANG |
| Affiliation: | 1. Institute of Applied Mathematics, College of Mathematics and Information Science, Henan University,Kaifeng 475001, Henan, China 2. Department of Mathematics, Nanjing University, Nanjing 210093, China |
| Abstract: | Abstract Basic facts for Gabor frame {E u(m)b T u(n)a g} m, n ∈ρ on local field are investigated. Accurately, that the canonical dual of frame {E u(m)b T u(n)a g} m, n ∈ρ also has the Gabor structure is showed; that the product ab decides whether it is possible for {E u(m)b T u(n)a g} m, n ∈ρ to be a frame for L 2(K) is discussed; some necessary conditions and two sufficient conditions of Gabor frame for L 2(K) are established. An example is finally given. *Project supported by the National Natural Science Foundation of China (No. 10571084, No. 10671062), the Postdoctoral Science Foundation of China (No. 2005037694) and the Natural Science Foundation of the Education Department of Henan Province of China (No. 2006110001). |
| Keywords: | Frame Gabor frame Local field |
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