Regular orbital measures on Lie algebras
Volume 113 / 2008
Colloquium Mathematicum 113 (2008), 1-11
MSC: Primary 58C35; Secondary 22E60, 43A70.
DOI: 10.4064/cm113-1-1
Abstract
Let $H_0$ be a regular element of an irreducible Lie algebra ${\mathfrak g}$, and let $\mu_{H_0}$ be the orbital measure supported on $O_{H_0}$. We show that $\widehat{\mu}_{H_0}^k\in L^2({\mathfrak g})$ if and only if $k>\dim{\mathfrak g} / (\dim{\mathfrak g}-\mathop{\rm rank}{\mathfrak g})$.
