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Fredholm spectrum and growth of cohomology groups

Jörg Eschmeier (2008)

Studia Mathematica

Let T ∈ L(E)ⁿ be a commuting tuple of bounded linear operators on a complex Banach space E and let σ F ( T ) = σ ( T ) σ e ( T ) be the non-essential spectrum of T. We show that, for each connected component M of the manifold R e g ( σ F ( T ) ) of all smooth points of σ F ( T ) , there is a number p ∈ 0, ..., n such that, for each point z ∈ M, the dimensions of the cohomology groups H p ( ( z - T ) k , E ) grow at least like the sequence ( k d ) k 1 with d = dim M.

Free CR distributions

Gerd Schmalz, Jan Slovák (2012)

Open Mathematics

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 n + n 2 for all n > 1. In...

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