| 关于Heisenberg不等式的几点说明(英文) |
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| 引用本文： | 于海波. 关于Heisenberg不等式的几点说明(英文)[J]. 高师理科学刊, 2007, 27(1): 16-17 |
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| 作者姓名： | 于海波 |
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| 作者单位： | 华东师范大学,数学系,上海,200062 |
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| 摘 要： | 设f(t)在区间[-a,a](a>0)一致连续,则(∫-+∞∞|f(t)|2dt)2≤4u2v2-A2,A=2(x0u-y0v),u2=∫-+∞∞t2|f(t)|2dt,v2=∫-+∞∞|f'(t)|2dt,x0=∫-+∞∞[f(t)/(1+t2)π]'dt和y0=∫-+∞∞[f'(t)/(1+t2)π]dt是有限的。
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| 关 键 词： | Heisenberg不等式 Weyl不等式 |
| 文章编号： | 1007-9831(2007)01-0016-02 |
| 修稿时间： | 2006-08-11 |
Remark on Heisenberg''''s inequality |
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| YU Hai-bo. Remark on Heisenberg''''s inequality[J]. Journal of Science of Teachers＇College and University, 2007, 27(1): 16-17 |
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| Authors: | YU Hai-bo |
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| Abstract: | Let f(t)be absolutely continuous in the interval[-a,a] for any a＞0,then(∫+∞-∞│f(t)|2dt)2＜-4||u||2||v||2-A2,where A=2(||x0u||-||y0v||),||u||2=∫+∞-++t2|f(t)|2dt,||v||2=∫+∞-∞|f'(t)|2dt,x0=∫+∞-∞[f(t)/(√(1+t2)π)]'dt ,x0=∫+∞-∞[f(t)/(√(1+t2)π)]'dt and y0=∫+∞-∞[f'(t)/(√(1+t2)π)]dt are all finite. |
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| Keywords: | Heisenberg's inequality Weyl's inequality |
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