Les automorphismes analytiques isométriques d'une variété complexe normée
Let G be a complex semi-simple group with a compact maximal group K and an irreducible holomorphic representation ρ on a finite dimensional space V. There exists on V a K-invariant Hermitian scalar product. Let Ω be the intersection of the unit ball of V with the G-orbit of a dominant vector. Ω is a generalization of the unit ball (case obtained for G = SL(n,C) and ρ the natural representation on Cn).We prove that for such manifolds, the Bergman and Szegö kernels as for the ball are rational fractions...
In this paper, we study a 5 dimensional configuration space of a 3-link snake robot model moving in a plane. We will derive two vector fields generating a distribution which represents a space of the robot’s allowable movement directions. An arbitrary choice of such generators generates the entire tangent space of the configuration space, i.e. the distribution is bracket-generating, but our choice additionally generates a finite dimensional Lie algebra over real numbers. This allows us to extend...
We give a formulation of certain types of mechanical systems using the structure of groupoid of the tangent and cotangent bundles to the configuration manifold ; the set of units is the zero section identified with the manifold . We study the Legendre transformation on Lie algebroids.
We call a unital locally convex algebra a continuous inverse algebra if its unit group is open and inversion is a continuous map. For any smooth action of a, possibly infinite-dimensional, connected Lie group on a continuous inverse algebra by automorphisms and any finitely generated projective right -module , we construct a Lie group extension of by the group of automorphisms of the -module . This Lie group extension is a “non-commutative” version of the group of automorphism...
Si introducono due strutture di gruppo di Lie su un dominio di Siegel omogeneo di . Per la palla unitaria si definisce una famiglia ad un parametro di strutture intermedie; ad ognuna di esse viene associato naturalmente un nucleo riproducente ottenendo un'interpolazione tra il nucleo di Bergman ed il nucleo di Szego.