Constructive approximation in de Branges-Rovnyak spaces

In most classical holomorphic function spaces on the unit disk, a function $f$ can be approximated in the norm of the space by its dilates f\_r(z):=f(rz)~(r \textless{} 1). We show that this is \emph{not} the case for the de Branges--Rovnyak spaces \cH(b). More precisely, we give an example of a non-extreme point $b$ of the unit ball of $H^\infty$ and a function f\in\cH(b) such that \lim\_{r\to1^-}\|f\_r\|\_{\cH(b)}=\infty. It is known that, if $b$ is a non-extreme point of the unit ball of $H^\infty$, then polynomials are dense in \cH(b). We give the first constructive proof of this fact

The skeleton of the staghorn coral Acropora millepora: molecular and structural characterization

15 pagesInternational audienceThe scleractinian coral Acropora millepora is one of the most studied species from the Great Barrier Reef. This species has been used to understand evolutionary, immune and developmental processes in cnidarians. It has also been subject of several ecological studies in order to elucidate reef responses to environmental changes such as temperature rise and ocean acidification (OA). In these contexts, several nucleic acid resources were made available. When combined to a recent proteomic analysis of the coral skeletal organic matrix (SOM), they enabled the identification of several skeletal matrix proteins, making A. millepora into an emerging model for biomineralization studies. Here we describe the skeletal microstructure of A. millepora skeleton, together with a functional and biochemical characterization of its occluded SOM that focuses on the protein and saccharidic moieties. The skeletal matrix proteins show a large range of isoelectric points, compositional patterns and signatures. Besides secreted proteins, there are a significant number of proteins with membrane attachment sites such as transmembrane domains and GPI anchors as well as proteins with integrin binding sites. These features show that the skeletal proteins must have strong adhesion properties in order to function in the calcifying space. Moreover this data suggest a molecular connection between the calcifying epithelium and the skeletal tissue during biocalcification. In terms of sugar moieties, the enrichment of the SOM in arabinose is striking, and the monosaccharide composition exhibits the same signature as that of mucus of acroporid corals. Finally, we observe that the interaction of the acetic acid soluble SOM on the morphology of in vitro grown CaCO3 crystals is very pronounced when compared with the calcifying matrices of some mollusks. In light of these results, we wish to commend Acropora millepora as a model for biocalcification studies in scleractinians, from molecular and structural viewpoints

A note on the stability of linear combinations of algebraic operators

The main purpose of this note is to characterize all the algebraic operators and having the same minimal polynomial and for which certain spectral properties of linear combinations of and do not depend on their coeffcients.peerReviewe

ZERO-FREE REGIONS FOR DIRICHLET SERIES

Abstract. In this paper, we are interested in explicit zero-free discs for some Dirichlet series and we also study a general Beurling-Nyman criterion for L-functions. Our results generalize and improve previous results obtained by N. Nikolski and by A. de Roton. As a concrete application, we get, for example, a Beurling-Nyman type criterion for the Siegel zero problem. 1