Summary: Smoothness of Densities on Compact Lie
School of Mathematics and Statistics,
University of Sheffield,
Hicks Building, Hounsfield Road,
Sheffield, England, S3 7RH
We give necessary and sufficient conditions for both square inte-
grability and smoothness for densities of a probability measure on a
compact connected Lie group.
Keywords and Phrases. Lie group, Haar measure, unitary dual,
Fourier transform, convolution operator, Lie algebra, weight, Sugiura
space, smooth density, central measure, infinitely divisible, deconvo-
lution density estimator.
AMS 2000 subject classification. 60B15, 43A05, 43A25, 43A77, 60E07
The study of probability measures on groups provides a mathematical frame-
work for describing the interaction of chance with symmetry. This subject