Localisation des singularités des fonctions analytiques définies par des séries du type $\Sigma {\mathbf{P}}_n\left(s\right)$exp$(-s{\lambda }_n$, où les ${\lambda }_n$ sont complexes et où les ${\mathbf{P}}_n\left(s\right)$ sont des polynômes tayloriens, en utilisant des propriétés obtenues selon deux méthodes originellement dues l’une à B. Lepson pour les séries d’exponentielles à coefficients polynomiaux et dont la suite des exposants est une $D$-suite et l’autre à G. L. Luntz pour les séries de Taylor-Dirichlet. Le résultat fondamental utilise un théorème de A. F. Leont’ev-G. P. Lapin...

This paper is devoted to studying the effects of a vanishing structural damping on the controllability properties of the one dimensional linear beam equation. The vanishing term depends on a small parameter $\epsilon \in (0,1)$. We study the boundary controllability properties of this perturbed equation and the behavior of its boundary controls $v_{\epsilon }$ as $\epsilon$ goes to zero. It is shown that for any time $T$ sufficiently large but independent of $\epsilon$ and for each initial data in a suitable space there exists a uniformly bounded...

This article considers the linear 1-d Schrödinger equation in (0,π) perturbed by a vanishing viscosity term depending on a small parameter ε > 0. We study the boundary controllability properties of this perturbed equation and the behavior of its boundary controls vε as ε goes to zero. It is shown that, for any time T sufficiently large but independent of ε and for each initial datum in H−1(0,π), there exists a uniformly...

This article considers the linear 1-d Schrödinger equation in (0,π) perturbed by a vanishing viscosity term depending on a small parameter ε > 0. We study the boundary controllability properties of this perturbed equation and the behavior of its boundary controls vε as ε goes to zero. It is shown that, for any time T sufficiently large but independent of ε and for each initial datum in H−1(0,π), there exists a uniformly...

We discuss relations between uniform minimality, unconditionality and interpolation for families of reproducing kernels in backward shift invariant subspaces. This class of spaces contains as prominent examples the Paley-Wiener spaces for which it is known that uniform minimality does in general neither imply interpolation nor unconditionality. Hence, contrarily to the situation of standard Hardy spaces (and of other scales of spaces), changing the size of the space seems necessary to deduce unconditionality...

Let $H\left(K\right)$ be the Hilbert space with reproducing kernel $K$. This paper characterizes some sufficient conditions for a sequence to be a universal interpolating sequence for $H\left(K\right)$.