The Singularity of Orbital Measures on Compact Lie Groups
Kathryn E. Hare and Wai Ling Yee
Source: Rev. Mat. Iberoamericana
Volume 20, Number 2
(2004), 517-530.
Abstract
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.
Primary Subjects: 43A80
Secondary Subjects: 22E46, 43A65
Keywords: orbital measures; compact Lie group; characters
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.rmi/1087482025
Zentralblatt MATH identifier:
02110197
Mathematical Reviews number (MathSciNet):
MR2073130
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