Multiplier Transformations on Compact Lie Groups and Algebras

Central Multiplier Theorems for Compact Lie Groups

The purpose of this note is to describe how central multiplier theorems for compact Lie groups can be reduced to corresponding results on a maximal torus. We shall show that every multiplier theorem for multiple Fourier series gives rise to a corresponding theorem for such groups and, also, for expansions in terms of special functions. We use the notation and terminology of N. J. Weiss [4]. Let...

Semiparametric estimation of rigid transformations on compact Lie groups

To cite this version: Bigot, Jérémie and Loubes, Jean-Michel and Vimond, Myriam Semiparametric estimation of shifts on compact Lie groups. (2008) In: 2nd MICCAI Workshop on Mathematical Foundations of Computational Anatomy, 6 September 2008 6 September 2008 (New York, United States). Open Archive Toulouse Archive Ouverte (OATAO) OATAO is an open access repository that collects the work of Toulo...

Hopf algebras of smooth functions on compact Lie groups

A C∞-Hopf algebra is a C∞-algebra which is also a convenient Hopf algebra with respect to the structure induced by the evaluations of smooth functions. We characterize those C∞-Hopf algebras which are given by the algebra C∞(G) of smooth functions on some compact Lie group G, thus obtaining an anti-isomorphism of the category of compact Lie groups with a subcategory of convenient Hopf algebras.

Notes on Lie Algebras and Lie Groups

Lie Algebras, Algebraic Groups, and Lie Groups

These notes are an introduction to Lie algebras, algebraic groups, and Lie groups in characteristic zero, emphasizing the relationships between these objects visible in their categories of representations. Eventually these notes will consist of three chapters, each about 100 pages long, and a short appendix. Single paper copies for noncommercial personal use may be made without explicit permiss...