Dirac delta function proof fourier space

[jhartc90]

Homework Statement

I am having trouble understanding this:

I have a Dirac Delta function

$$ \delta (t_1-t_2) $$

but I want to prove that in the frequency domain (Fourier Space), it is:

$$\delta(\omega_1+\omega_2) $$

Would anyone have any ideas how to go about solving this problem?

I know that t1 and t2 are two independent times, and that w1 and w2 are two independent frequencies. But I do not fully understand what this question wants/is asking?

Homework Equations

[/B]
The only relevant equations I could think of may just be transforms found in a table.

The Attempt at a Solution

Hard for me to attempt when I don't really understand what the question means,

 

[Orodruin]

The Dirac delta distribution is what it is. It is unclear what you mean by it "being" ##\delta(t_1-t_2)##, this is just insertion of some argument. A delta distribution in real space has a Fourier transform which is of the form ##e^{i\omega t_0}## and not another delta distribution.

In order for us to help you, you need to specify your problem better. In particular, you need to provide the problem itself where this appeared and keep the wording exactly as provided.

 

[jhartc90]

I attached the file. We are suppose to also state any assumptions we make.

 

[Orodruin]

I believe we need more context than this. It is not clear to me how to interpret this question and for the interpretations I can think of it does not make sense.

 

[jhartc90]

I believe we need more context than this. It is not clear to me how to interpret this question and for the interpretations I can think of it does not make sense.

It is in time and not space. We have a 2D Fourier transform. If the function is transformed correctly twice, due to two times and two frequencies, the answer should be able to be obtained.

 

[jhartc90]

I think i may have figured it out, perhaps the thread should be closed?