# 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}
}
• A. Olofsson
• Published 8 May 2010
• Mathematics
• Acta Mathematica Hungarica
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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