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The singularity of orbital measures on compact Lie groups.

Kathryn E. HareWai Ling Yee — 2004

Revista Matemática Iberoamericana

We find the minimal real number k such that the kth power of the Fourier transform of any continuous, orbital measure on a classical, compact Lie group belongs to l2. This results from an investigation of the pointwise behaviour of characters on these groups. An application is given to the study of Lp-improving measures.

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