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Conference Papers Year : 2015

Cyclicity in the harmonic Dirichlet space


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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hal-01261077 , version 1 (23-01-2016)



Evgueni Abakumov, Omar El-Fallah, Karim Kellay, Thomas Ransford. Cyclicity in the harmonic Dirichlet space. Conference on Harmonic and Functional, Analysis, Operator Theory and Applications. 1–10, Theta Ser. Adv. Math., 19, Theta, Bucharest, 2017., Jun 2015, Bordeaux, France. ⟨hal-01261077⟩
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