Homogeneous distribution

A distribution $u$ is homogeneous of degree $\sigma$ when ${\delta }_{t}u=t^{\sigma }u$ for every $t>0$. With the unnormalized angular-frequency convention, its Fourier transform is homogeneous of degree $-n-\sigma$.

The scaling property of the Fourier transform extends by duality toConsequently a homogeneous distribution of degree $\sigma$ transforms into one of degree $-n-\sigma$.