Cyclicity in the harmonic Dirichlet space
2015
The harmonic Dirichlet space $\cD(\TT)$ is the Hilbert space of functions $f\in L^2(\TT)$ such that
$$
\|f\|_{\cD(\TT)}^2:=\sum_{n\in\ZZ}(1+|n|)|\hat{f}(n)|^2<\infty.
$$
We give sufficient conditions for $f$ to be cyclic in $\cD (\TT)$, in other words, for $\{\zeta ^nf(\zeta):\ n\geq 0\}$ to span a dense subspace of $\cD(\TT)$.
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