# Cyclicité dans les espaces de fonctions analytiques

Emmanuel Fricain
LPP, Université de Lille
http://math.univ-lille1.fr/~fricain/

Date(s) : 12/05/2014   iCal
10 h 00 min - 11 h 00 min

Cyclicity in the spaces of analytic functions

We introduce a large family of reproducing kernel Hilbert spaces $${\mathcal {H}} \subset \hbox {Hol}({\mathbb {D}})$$, which include the classical Dirichlet-type spaces $$\mathcal {D}_\alpha$$, by requiring normalized monomials to form a Riesz basis for $${\mathcal {H}}$$. Then, after precisely evaluating the $$n$$th optimal norm and the $$n$$-th approximant of $$f(z)=1-z$$, we completely characterize the cyclicity of functions in $$\hbox {Hol}(\overline{\mathbb {D}})$$ with respect to the forward shift.

https://arxiv.org/abs/1312.7739

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