# Integral homework problems

Apteronotus
Hi everyone,

Can anyone show me how the property
$$\frac{1}{2\pi} \int ^{\infty} _{-\infty} e^{i\omega x}d\omega= \delta(x)$$
holds.

Thanks,

g_edgar

Do you know about Schwartz distribution theory? Generalized functions? Because that is what you are writing about, not traditional calculus functions. Your equation MEANS...

$$\frac{1}{2\pi}\int_{-\infty}^\infty e^{i\omega x} \phi(x)\,d\omega = \phi(x)$$

for all test functions $\phi$ from an appropriate class.

Apteronotus