International audienceWe prove that l(2) contains vectors which are hypercyclic simultaneously for all multiples of the backward shift operator by constants of absolute value greater than 1. The set of such vectors is dense G(delta). (C) 2002 Elsevier Science (USA). All rights reserved

Abstract. We study the localization of zeros for Cauchy transforms of discrete measures on the real line. This question is motivated by the theory of canonical systems of differential equations. In particular, we prove that the spaces of Cauchy transforms having the localization property are in one-to-one correspondence with the canonical systems of special type, namely, those whose Hamiltonians consist only of indivisible intervals accumulating on the left. Various aspects of the localization phenomena are studied in details. Connections with the density of polynomials and other topics in analysis are discussed.

Let H (B d ) denote the space of holomorphic functions on the unit ball B d of C d . Given a radial doubling weight w, we construct functions f, g ∈ H (B 1 ) such that | f | + |g| is comparable to w. Also, we obtain similar results for B d , d ≥ 2, and for circular, strictly convex domains with smooth boundary. As an application, we study weighted composition operators and related integral operators on growth spaces of holomorphic functions.

Let Hol(D) denote the space of holomorphic functions on the unit disk D. We characterize those radial weights w on D for which there exist functions f, g ∈ Hol(D) such that the sum |f | + |g| is equivalent to w. Also, we obtain similar results in several complex variables for circular, strictly convex domains with smooth boundary.