A note on infinitesimal generators and potential operators of contraction semigroups

Infinitesimal Generators Associated with Semigroups of Linear Fractional Maps

We characterize the infinitesimal generator of a semigroup of linear fractional self-maps of the unit ball in C, n ≥ 1. For the case n = 1 we also completely describe the associated Koenigs function and we solve the embedding problem from a dynamical point of view, proving, among other things, that a generic semigroup of holomorphic self-maps of the unit disc is a semigroup of linear fractional...

A Note on Operators of Deletion and Contraction for Antichains

A Note on the Spectral Operators of Scalar Type and Semigroups of Bounded Linear Operators

It is shown that, for the spectral operators of scalar type, the well-known characterizations of the generation of C0and analytic semigroups of bounded linear operators can be reformulated exclusively in terms of the spectrum of such operators, the conditions on the resolvent of the generator being automatically met and the corresponding semigroup being that of the exponentials of the operator.

Pluripotential Theory, Semigroups and Boundary Behavior of Infinitesimal Generators in Strongly Convex Domains

We characterize infinitesimal generators of semigroups of holomorphic selfmaps of strongly convex domains using the pluricomplex Green function and the pluricomplex Poisson kernel. Moreover, we study boundary regular fixed points of semigroups. Among other things, we characterize boundary regular fixed points both in terms of the boundary behavior of infinitesimal generators and in terms of plu...

The Infinitesimal Stability of Semigroups

The concept of C°° infinitesimal stability for representations of a semigroup by C maps is defined. In the case of expanding linear maps of the torus T it is shown that certain algebraic conditions assure such stability.