Question

The sinc function defines a tempered distribution

Answer 1

Step-by-step explanation:

need to check if the function |sin(x)| defines a tempered distribution and find the fourier transform of the distribution.

I think it defines it because it is summable on every compact subset and I have also found its first distributional derivative, which is:

f′(x)=sin(x)cos(x)|sin(x)|

but I am clueless on how to find the F transform.

I know the for a tempered distribution, if ϕ is a test function then:

⟨T^,ϕ⟩=⟨T,ϕ^⟩

and

Dαϕˆ=(i2πk)αϕ^

but I am not able to use these rules to complete the problem.