Functional Calculus for Infinitesimal Generators of Holomorphic 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...

Wiener Integral Representations for Certain Semigroups Which Have Infinitesimal Generators with Matrix Coefficients

Holomorphic Functional Calculus and Some Applications

In this note, we present some applications of complex analysis to functional analysis and operator theory. We will focus on some basic facts of holomorphic functional calculus and its applications to analyze the spectrum of operators.

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.

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...