Cantor sets and cyclicity in weighted Dirichlet spaces

Omar El-Fallah (1) , Karim Kellay (2) , Thomas Ransford (3)

1 Département de Mathématiques
2 LATP - Laboratoire d'Analyse, Topologie, Probabilités
3 Department of Mathematical Sciences

We treat the problem of characterizing the cyclic vectors in the weighted Dirichlet spaces, extending some of our earlier results in the classical Dirichlet space. The absence of a Carleson-type formula for weighted Dirichlet integrals necessitates the introduction of new techniques.

Mots clés: Cantor set; Dirichlet space; weight; cyclic vector; $\alpha$-capacity

Domaines: Variables complexes [math.CV]; Analyse classique [math.CA]

Omar El-Fallah, Karim Kellay, Thomas Ransford. Cantor sets and cyclicity in weighted Dirichlet spaces. Journal of Mathematical Analysis and Applications, 2010, 372, pp.565-573. ⟨hal-00450747⟩