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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