
#1
Nov1710, 08:47 AM

P: 196

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: 608

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: 196

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? 


Register to reply 
Related Discussions  
Is the ordinary integral a special case of the line integral?  Calculus  3  
volume integral to spherical coords to contour integral  Calculus & Beyond Homework  4  
Is Cauchy's integral formula applicable to this type of integral?  Calculus & Beyond Homework  4  
Length of the curve integral, can't solve the integral  Calculus & Beyond Homework  2  
Changing cartesian integral to polar integral  Calculus  1 