Multivariable approximate Carleman-type theorems for complex measures

We prove a multivariable approximate Carleman theorem on the determination of complex measures on ${\mathbb{R}}^n$ and ${\mathbb{R}}^n_+$ by their moments. This is achieved by means of a multivariable Denjoy--Carleman maximum principle for quasi-analytic functions of several variables. As an application, we obtain a discrete Phragm\'{e}n--Lindel\"{o}f-type theorem for analytic functions on ${\mathbb{C}}_+^n$.Comment: Published at http://dx.doi.org/10.1214/009117906000000377 in the Annals of Probability (http://www.imstat.org/aop/) by the Institute of Mathematical Statistics (http://www.imstat.org

An Extremal Problem for Characteristic Functions

Suppose E is a subset of the unit circle T and Hinfinity C Linfinity is the Hardy subalgebra. We examine the problem of finding the distance from the characteristic function of E to znHinfinity. This admits an alternate description as a dual extremal problem. Precise solutions are given in several important cases. The techniques used involve the theory of Toeplitz and Hankel operators as well as the construction of certain conformal mappings

Semiflow of analytic functions and semigroups of composition operators

The study of analytic semiflows on the open unit disc and the particular form of its infinitesimal generator $G$ makes possible the study of semigroups of composition operators $(T(t))_{t\geq 0}$ on various well-known spaces of holomorphic functions such as Hardy, Dirichlet and Bergman spaces. We will provide compactness, analyticity and invertibility complete characterization of $(T(t))_{t\geq 0}$ in terms of $G$