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macauor

银虫 (小有名气)

[求助] 积分函数为f(x)*delta(x)*delta(x),积分域为负无穷到正无穷,等于多少

如题,delta(x) 为狄拉克delta函数,积分用到了积分函数为 f(x)*delta(x)*delta(x),这两个delta(x)相乘怎么处理?
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macauor

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引用回帖:
4楼: Originally posted by feixiaolin at 2014-09-13 07:24:53
f(x)*delta(x)*delta(x)=【f(0)*delta(x)】*delta(x)=f(0)*delta(x)
积分:
Int=f(0)*step(x)   阶跃函数
Int=f(0)           一个数...

版主的积分结果有啥参考资料没?
5楼2014-09-13 12:50:27
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feixiaolin

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f(x)*delta(x)*delta(x)=【f(0)*delta(x)】*delta(x)=f(0)*delta(x)
积分=f(0)*step(x)   阶跃函数
2楼2014-09-12 22:55:23
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hank612

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★ ★ ★ ★ ★
macauor(feixiaolin代发): 金币+5 2014-09-13 21:29:53
引用回帖:
2楼: Originally posted by feixiaolin at 2014-09-12 22:55:23
f(x)*delta(x)*delta(x)=【f(0)*delta(x)】*delta(x)=f(0)*delta(x)
积分=f(0)*step(x)   阶跃函数

版主大神, 定积分后应该不再是函数, 应该是个数才对.

如果用阶段函数 g_a(x)= 0  if |x|>a/2;  1/a if |x|<=a/2, a为很小的正数
来取代 delta函数, 立得积分值为f(0)/a, 因此a趋于零时,定积分为无穷大. 并且无穷大的符号等于 f(0)的符号.
We_must_know. We_will_know.
3楼2014-09-13 06:53:09
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feixiaolin

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引用回帖:
3楼: Originally posted by hank612 at 2014-09-13 06:53:09
版主大神, 定积分后应该不再是函数, 应该是个数才对.

如果用阶段函数 g_a(x)= 0  if |x|>a/2;  1/a if |x|<=a/2, a为很小的正数
来取代 delta函数, 立得积分值为f(0)/a, 因此a趋于零时,定积分为 ...

f(x)*delta(x)*delta(x)=【f(0)*delta(x)】*delta(x)=f(0)*delta(x)
积分:
Int[f(x)*delta(x)*delta(x), {x, -inf, x}]=f(0)*step(x)   阶跃函数
Int[f(x)*delta(x)*delta(x), {x, -inf, +inf}]=f(0)           一个数
4楼2014-09-13 07:24:53
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