[再寄小读者之数学篇](2014-09-22 distributions and square integrable functions)

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Suppose that $f\in L^2$, $g\in \scrD‘$, if $$\bex f=g,\mbox{ in }\scrD‘, \eex$$ then $f=g\in L^2$.

In fact, $\scrD\subset L^2 \ra L^2\subset\scrD‘$. Thus $h=f-g=0\in \scrD‘$, the zero element is the same in $L^2$ and $\scrD‘$, and hence $h=f-g=0\in L^2$, $g=f-(f-g)\in L^2$. 

[再寄小读者之数学篇](2014-09-22 distributions and square integrable functions)

标签：style   color   io   os   ar   sp   2014   on   c   

原文地址：http://www.cnblogs.com/zhangzujin/p/3998036.html