Associative property of convolution

[sainistar]

Hi There

The associative property of convolution is proved in literature for infinite interval. I want to prove the associative property of convolution for finite interval. I have explained the problem in the attached pdf file.

Any help is appreciated.

Regards
Aman

 

[micromass]

Integral (10) is obviously wrong. Your two integrals have $\theta$ in their bounds. But $\theta$ is an integration variable! This can't be correct.

Why do you obtain something wrong here. Because after equation (3) they applied Fubini and switched the both integrals, and THEN they did the substitution.

You must do something similar. Apply Fubini after (9). But Fubini will in this case not be simply switching the integral signs...

 

[sainistar]

Thanks micromass

I was looking for the Fubini theorem when the bound are the integration variable. I did not find any. Can you please let me know any source i can read.
It will also be helpful if you can suggest how can i apply Fubini after (9).

Regards