I was verifying that:(adsbygoogle = window.adsbygoogle || []).push({});

http://en.wikipedia.org/wiki/Convolution#Integration

But, I'd like to know if this equality is true:

[tex]\int f(x)g(x)dx \overset{?}{=} \int f(x)dx \ast \int g(x)dx[/tex]

Subquestion: this theorem above can be applied in summation too?

[tex]\sum_{x}\left (f(x)\ast f(x) \right )\overset{?}{=}\left(\sum_{x} f(x)\right)\left (\sum_{x} g(x) \right )[/tex]

[tex]\sum_{x}f(x)g(x) \overset{?}{=} \sum_{x}f(x) \ast \sum_{x}g(x)[/tex]

Thanks!

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# Convulation and integration

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