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Integral homework problems 
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#1
Nov1710, 08:47 AM

P: 203

Hi everyone,
Can anyone show me how the property [tex]\frac{1}{2\pi} \int ^{\infty} _{\infty} e^{i\omega x}d\omega= \delta(x)[/tex] holds. Thanks, 


#2
Nov1710, 09:32 AM

P: 607

Do you know about Schwartz distribution theory? Generalized functions? Because that is what you are writing about, not traditional calculus functions. Your equation MEANS...
[tex] \frac{1}{2\pi}\int_{\infty}^\infty e^{i\omega x} \phi(x)\,d\omega = \phi(x) [/tex] for all test functions [itex]\phi[/itex] from an appropriate class. 


#3
Nov1710, 11:15 AM

P: 203

edgar thanks for your reply.
It seems I've stumbled on something beyond my means. I dont know anything about Schwartz distribution theory and a quick search on the net didnt help at all. I thought the integral would be an easy calculus identity of sorts. Can you show me why the integral holds? 


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