The Singularity of Orbital Measures on Compact Lie Groups

  • Kathryn E. Hare

    University of Waterloo, Waterloo, Canada
  • Wai Ling Yee

    Massachusetts Institute of Technology, Cambridge, USA

Abstract

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. 517–530

DOI 10.4171/RMI/399