Answer to Question #97504 in Calculus for Rachel

Answer to Question #97504 in Calculus for Rachel

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Question #97504

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

Expert’s answer

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

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