We find the minimal real number such that the th power of the Fourier transform of any continuous, orbital measure on a classical, compact Lie group belongs to . This results from an investigation of the pointwise behaviour of characters on these groups. An application is given to the study of -improving measures.
Cite this article
Kathryn E. Hare, Wai Ling Yee, The Singularity of Orbital Measures on Compact Lie Groups. Rev. Mat. Iberoam. 20 (2004), no. 2, pp. 517–530DOI 10.4171/RMI/399