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In mathematics, a 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. It can be a non-trivial problem to extend a given homogeneous distribution from Rn \ {0} to a distribution on Rn, although this is necessary for many of the techniques of Fourier analysis, in particular the Fourier transform, to be brought to bear. Such an extension exists in most cases, however, although it may not be unique.s, however, although it may not be unique.
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| rdfs:comment |
In mathematics, a 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.bles. The number m can be real or complex.
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Homogeneous distribution
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