The Fourier Transformations of Positive Distributions on Lorentz Group SO(3,1)

摘要

With the aid of Plancherel|Godement Theorem, we prove that every positive distribution T on SO(3,1) which is bi|invariant under SO(3) corresponds to a measure μ on Ω={s∈C|s(2-s)≥0}, and μ can be decomposed into μ=μ 1+μ 2 , where μ 1 is a bounded measure on 0≤s≤2 and μ 2 is a slowly increasing measure on {s∈C| Re (s)=1}.