Smoothness of Densities on Compact Lie Groups

zbMATH Open1326.60010arXiv1109.3051MaRDI QIDQ5500293

Publication date: 5 August 2015

Abstract: We give necessary and sufficient conditions for both square integrability and smoothness for densities of a probability measure on a compact connected Lie group.

Full work available at URL: https://arxiv.org/abs/1109.3051

zbMATH Keywords

Fourier transform infinitely divisible Lie algebra Lie group convolution operator Haar measure weight unitary dual smooth density central measure deconvolution density estimator Sugiura space

Mathematics Subject Classification ID

Infinitely divisible distributions; stable distributions (60E07) Measures on groups and semigroups, etc. (43A05) Fourier and Fourier-Stieltjes transforms on locally compact and other abelian groups (43A25) Probability measures on groups or semigroups, Fourier transforms, factorization (60B15) Harmonic analysis on general compact groups (43A77)