- #1

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I am really struggling to prove that

"The integral of the convolution between functions f and gequals the product of their integrals", http://en.wikipedia.org/wiki/Convolution#Integration

Can anybody give me a hint?

Many thanks

- Thread starter muzialis
- Start date

- #1

- 166

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I am really struggling to prove that

"The integral of the convolution between functions f and gequals the product of their integrals", http://en.wikipedia.org/wiki/Convolution#Integration

Can anybody give me a hint?

Many thanks

- #2

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What did you try?? Where are you stuck?

- #3

mathman

Science Advisor

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∫{∫f(y)g(x-y)dy}dx = ∫f(y){∫g(y-x)dx}dy (Fubini)

= ∫f(y){∫g(u)du)}dy = ∫f(y)dy∫g(u)du

- #4

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Thanks very muhc for your help.

I was following the line given by Mathman, but did not realize that the variable translation would not affcet the value of the integral as the integration domain is the whole real line, many thanks

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