Regular Orbital Measures on Lie Algebras

Details Regular Orbital Measures on Lie Algebras Regular Orbital Measures on Lie Algebras

2009-02-11

arxiv.org/abs/0902.1909v1

Colloq. Math. 113 (2008), no. 1, 1--11

Mathematics

Functional Analysis

Scientific paper

Let H be a regular element of an irreducible Lie Algebra g, and let mu be the
orbital measure supported on the Adjoint orbit of H. We show that the k-th
power of the Fourier transform of mu is in L^2(g) if and only if k > dim g/(dim
g-rank g).

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