Journée d'analyse

Une journée d'analyse sera organisée le vendredi 6 juin.

Lieu : salle Kampé de Fériet, 1er étage, Bâtiment M2

Organisateurs : Catalin Badea, Noé de Rancourt, Maëva Ostermann

Programme :

9h30 - 10h : Café d'accueil

10h - 10h50 : Oliver Roth (université de Würzburg) : A refinement of Jorgensen's Theorem and the Gauss-Lucas-Thurston Theorem in hyperbolic geometry

11h - 11h50 : Daniel Seco (université de La Laguna, Tenerife) : Towards spectral descriptions of cyclic functions

12h15 - 14h15 : Déjeuner

14h30 - 15h20 : Sibel Şahin (université des beaux-arts Mimar-Sinan, Istanbul) : Size of Parameter Set and The Set of Disjoint Hypercyclic Vectors

Résumés :

Oliver Roth, A refinement of Jorgensen's Theorem and the Gauss-Lucas-Thurston Theorem in hyperbolic geometry

Abstract:  By a classical result of Jorgensen every geodesic in a simply connected hyperbolic domain G which touches an Euclidean disk in G does not intersect the interior of that disk. We give a refinement of this result that takes into account point singularities of the underlying geometric structure. As an application we extend the Gauss-Lucas-Thurston Theorem from Euclidean to hyperbolic geometry viz. from polynomials to Blaschke products.

This is joint work with Daniela Kraus, Javad Mashreghi and Annika Moucha.

Daniel Seco, Towards spectral descriptions of cyclic functions

We build on a characterization of inner functions f due to Le, in terms of the spectral properties of the operator V=M_f*M_f and study to what extent the cyclicity on weighted Hardy spaces H²_ω of the function z ↦ a-z can be inferred from the spectral properties of analogous operators V_a. We describe several properties of the spectra that hold in a large class of spaces and then, we focus on the particular case of Bergman-type spaces, for which we describe completely the spectrum of such operators and find all eigenfunctions. This is a joint work with Miguel Monsalve.

Sibel Şahin, Size of Parameter Set and The Set of Disjoint Hypercyclic Vectors

In this talk we will consider the relation between the set of common disjoint-hypercyclic (d-HC) vectors for families of linear operators acting on a Banach space X and the size of parameter set that parametrizes these operators. When the parameter set is uncountable, the non emptiness of the set of common d-HC vectors is a non trivial question and the literature about the hypercyclic counterpart of this question shows us that there are strict restrictions on the size of parameter set. Throughout the talk we will examine this general framework over different examples of commonly encountered linear operators namely weighted shifts, translations, composition and differential operators.