Answer to Question #97504 in Calculus for Rachel

Question

Let a be a multi-index. Compute the Fourier transform of D^(a)δ.

Answer 1

Fourier Transform of $\delta^a$ is

(2πi)^|a| * x^a * F({\delta ^}a )
= (2πi)^|a| * x^a * 1
= (2πi)^|a| * x^a 
Therefore, 
Fourier Transform of D^a(\delta) is
\frac{1}{(2πi)^|a|} * {\delta}^a