About: Homogeneous distribution

In mathematics, a homogeneous distribution is a distribution S on Euclidean space Rn or Rn \ {0} that is homogeneous in the sense that, roughly speaking, for all t > 0. More precisely, let be the scalar division operator on Rn. A distribution S on Rn or Rn \ {0} is homogeneous of degree m provided that for all positive real t and all test functions φ. The additional factor of t−n is needed to reproduce the usual notion of homogeneity for locally integrable functions, and comes about from the Jacobian change of variables. The number m can be real or complex.