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Smoothness of Densities on Compact Lie David Applebaum,

Summary: Smoothness of Densities on Compact Lie
David Applebaum,
School of Mathematics and Statistics,
University of Sheffield,
Hicks Building, Hounsfield Road,
Sheffield, England, S3 7RH
e-mail: D.Applebaum@sheffield.ac.uk
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
1 Introduction
The study of probability measures on groups provides a mathematical frame-
work for describing the interaction of chance with symmetry. This subject


Source: Applebaum, David - Department of Probability and Statistics, University of Sheffield


Collections: Mathematics