# On the shift semigroup on the Hardy space of Dirichlet series

@article{Olofsson2010OnTS, title={On the shift semigroup on the Hardy space of Dirichlet series}, author={Anders Olofsson}, journal={Acta Mathematica Hungarica}, year={2010}, volume={128}, pages={265-286} }

AbstractWe develop a Wold decomposition for the shift semigroup on the Hardy space $$
\mathcal{H}^2
$$ of square summable Dirichlet series convergent in the half-plane $$
\Re (s) > 1/2
$$. As an application we have that a shift invariant subspace of $$
\mathcal{H}^2
$$ is unitarily equivalent to $$
\mathcal{H}^2
$$ if and only if it has the form $$
\phi \mathcal{H}^2
$$ for some $$
\mathcal{H}^2
$$-inner function φ.

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