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| Basic Results of Gabor Frame on Local Fields |
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Citation： |
Dengfeng LI,Huikun JIANG.Basic Results of Gabor Frame on Local Fields[J].Chinese Annals of Mathematics B,2007,28(2):165~176 |
| Page view： 1177
Net amount： 840 |
Authors： |
Dengfeng LI; Huikun JIANG |
Foundation： |
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). |
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| Abstract： |
Basic facts for Gabor frame $\{E_{u(m)b}T_{u(n)a}g\}_{m,\,n\in\, {\mathbf P}}$ on local field are investigated. Accurately, that the canonical dual of frame $\{E_{u(m)b}T_{u(n)a}g\}_{m,n\in{\mathbf P}}$ also has the Gabor structure is showed; that the product $ab$ decides whether it is possible for $\{\!E_{u(m)b}T_{u(n)a}g\}_{m,n\in{\mathbf P}}$ 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. |
Keywords： |
Frame, Gabor frame, Local field |
Classification： |
42C15, 42C40 |
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