Revista Matemática Iberoamericana


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Volume 20, Issue 2, 2004, pp. 517–530
DOI: 10.4171/RMI/399

Published online: 2004-08-31

The Singularity of Orbital Measures on Compact Lie Groups

Kathryn E. Hare[1] and Wai Ling Yee

(1) University of Waterloo, Waterloo, Canada

We find the minimal real number $k$ such that the $k$th power of the Fourier transform of any continuous, orbital measure on a classical, compact Lie group belongs to $l^{2}$. This results from an investigation of the pointwise behaviour of characters on these groups. An application is given to the study of $L^{p}$-improving measures.

Keywords: Orbital measures, compact Lie group, characters

Hare Kathryn, Yee Wai Ling: The Singularity of Orbital Measures on Compact Lie Groups. Rev. Mat. Iberoam. 20 (2004), 517-530. doi: 10.4171/RMI/399