Geodesic
The size of characters of compact Lie groups
Studia Mathematica, Tome 129 (1998) no. 1, pp. 1-18
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Pointwise upper bounds for characters of compact, connected, simple Lie groups are obtained which enable one to prove that if μ is any central, continuous measure and n exceeds half the dimension of the Lie group, then $μ^n ∈ L^1$. When μ is a continuous, orbital measure then $μ^n$ is seen to belong to $L^2$. Lower bounds on the p-norms of characters are also obtained, and are used to show that, as in the abelian case, m-fold products of Sidon sets are not p-Sidon if p 2m/(m+1). 
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Kathryn E. Hare. The size of characters of compact Lie groups. Studia Mathematica, Tome 129 (1998) no. 1, pp. 1-18. doi: 10.4064/sm-129-1-1-18

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