Formules intégrales pour les formes différentielles sur , I
Let T ∈ L(E)ⁿ be a commuting tuple of bounded linear operators on a complex Banach space E and let be the non-essential spectrum of T. We show that, for each connected component M of the manifold of all smooth points of , there is a number p ∈ 0, ..., n such that, for each point z ∈ M, the dimensions of the cohomology groups grow at least like the sequence with d = dim M.
There are only some exceptional CR dimensions and codimensions such that the geometries enjoy a discrete classification of the pointwise types of the homogeneous models. The cases of CR dimensions n and codimensions n 2 are among the very few possibilities of the so-called parabolic geometries. Indeed, the homogeneous model turns out to be PSU(n+1,n)/P with a suitable parabolic subgroup P. We study the geometric properties of such real (2n+n 2)-dimensional submanifolds in for all n > 1. In...