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arXiv · 1312.7739

Cyclicity in reproducing kernel Hilbert spaces of analytic functions

Emmanuel Fricain·Javad Mashreghi·Daniel Seco
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Abstract

We introduce a large family of reproducing kernel Hilbert spaces $\mathcal{H} \subset \mbox{Hol}(\mathbb{D})$, 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 $\mbox{Hol}(\overline{\mathbb{D}})$ with respect to the forward shift.

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Emmanuel Fricain, Javad Mashreghi, Daniel Seco. 2013-12-30. Cyclicity in reproducing kernel Hilbert spaces of analytic functions. https://arxiv.org/abs/1312.7739

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