Regular orbital measures on Lie algebras

DOI10.4064/CM113-1-1zbMath1155.22018arXiv0902.1909OpenAlexW2963942731MaRDI QIDQ5457789

Alex Wright

Publication date: 14 April 2008

Published in: Colloquium Mathematicum (Search for Journal in Brave)

Abstract: Let H be a regular element of an irreducible Lie Algebra g, and let mu be the orbital measure supported on the Adjoint orbit of H. We show that the k-th power of the Fourier transform of mu is in L^2(g) if and only if k > dim g/(dim g-rank g).

Full work available at URL: https://arxiv.org/abs/0902.1909

zbMATH Keywords

Lie algebrasorbital measures

Mathematics Subject Classification ID

Integration on manifolds; measures on manifolds (58C35) Lie algebras of Lie groups (22E60) Analysis on specific locally compact and other abelian groups (43A70)

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