Continuous homomorphisms on and Ramsey theory.
Continuous lattices and compact Lawson semilattices.
Continuous measures on compact Lie groups
We study continuous measures on a compact semisimple Lie group using representation theory. In Section 2 we prove a Wiener type characterization of a continuous measure. Next we construct central measures on which are related to the well known Riesz products on locally compact abelian groups. Using these measures we show in Section 3 that if is a compact set of continuous measures on there exists a singular measure such that is absolutely continuous with respect to the Haar measure on...
Continuous transformation groups on spaces
A differentiable group is a group in the category of (reduced and nonreduced) differentiable spaces. Special cases are the rationals ℚ, Lie groups, formal groups over ℝ or ℂ; in general there is some mixture of those types, the general structure, however, is not yet completely determined. The following gives as a corollary a first essential answer. It is shown, more generally,that a locally compact topological transformation group, operating effectively on a differentiable space X (which satisfies...
Continuously factorable groupoids.
Contractibilité du groupe linéaire des espaces de Hilbert de dimension infinie
Contraction of an adapted functional calculus.
Contraction semigroups and representations.
Contractions de groupes de Lie semi-simples sur le groupe de Poincaré généralisé
Contractions of to the Heisenberg group and Berezin calculus. (Contraction de vers le groupe de Heisenberg et calcul de Berezin.)
Contractive Automorphisms on Locally Compact Groups.
Contribution of noncommutative geometry to index theory on singular manifolds
This survey of the work of the author with several collaborators presents the way groupoids appear and can be used in index theory. We define the general tools, and apply them to the case of manifolds with corners, ending with a topological index theorem.
Contributions to the duality theory of abelian topological groups and to the theory of nuclear groups [Book]
Control systems on semi-simple Lie groups and their homogeneous spaces
In the present paper, we consider the class of control systems which are induced by the action of a semi-simple Lie group on a manifold, and we give a sufficient condition which insures that such a system can be steered from any initial state to any final state by an admissible control. The class of systems considered contains, in particular, essentially all the bilinear systems. Our condition is semi-algebraic but unlike the celebrated Kalman criterion for linear systems, it is not necessary. In...
Control Systems on the Orthogonal Group SO(4)
We classify the left-invariant control affine systems evolving on the orthogonal group . The equivalence relation under consideration is detached feedback equivalence. Each possible number of inputs is considered; both the homogeneous and inhomogeneous systems are covered. A complete list of class representatives is identified and controllability of each representative system is determined.
Controllability of affine right-invariant systems on solvable Lie groups.
Controllability of invariant control systems at uniform time
Let be a compact and connected semisimple Lie group and an invariant control systems on . Our aim in this work is to give a new proof of Theorem 1 proved by Jurdjevic and Sussmann in [6]. Precisely, to find a positive time such that the system turns out controllable at uniform time . Our proof is different, elementary and the main argument comes directly from the definition of semisimple Lie group. The uniform time is not arbitrary. Finally, if denotes the reachable set from arbitrary...
Controllability of right invariant systems on semi-simple Lie groups
We deal with controllability of right invariant control systems on semi-simple Lie groups. We recall the history of the problem and the successive results. We state the final complete result, with a sketch of proof.
Controllability of systems on a nilpotent Lie group
Controllability on real reductive Lie groups.