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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    Journal of the London Mathematical Society
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The classical completeness problem raised by Beurling and independently by Wintner asks for which ψ∈L2(0,1) , the dilation system {ψ(kx):k=1,2,…} is complete in L2(0,1) , where ψ is identified with
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