Analysis on compact Lie groups of large dimension and on connected compact groups

Analysis on compact Lie groups of large dimension and on connected compact groups

The study of Gaussian convolution semigroups is a subject at the crossroad between abstract and concrete problems in harmonic analysis. This article suggests selected open problems that are in large part motivated by joint work with Alexander Bendikov. This paper is dedicated to the memory of Andrzej Hulanicki. My first scientific encounter with Andrzej was through his students, which is fittin...

Probability on Compact Lie Groups

Compact Lie Groups

The first half of the paper presents the basic definitions and results necessary for investigating Lie groups. The primary examples come from the matrix groups. The second half deals with representation theory of groups, particularly compact groups. The end result is the Peter-Weyl theorem.

Towards coordination algorithms on compact Lie groups

The present work considers the design of control algorithms to coordinate a swarm of identical, autonomous, cooperating agents that evolve on compact Lie groups. The objective is that the agents reach a so-called consensus state without using any external reference. In the same line of thought, a leader-follower approach where ’follower’ agents would track one ’leader’ agent is excluded, in fav...

Lie Groups and p-Compact Groups

A p-compact group is the homotopical ghost of a compact Lie group; it is the residue that remains after the geometry and algebra have been stripped away. This paper sketches the theory of p-compact groups, with the intention of illustrating the fact that many classical structural properties of compact Lie groups depend only on homotopy theoretic considerations. 1 From compact Lie groups to p-co...