A Hilbert space of Dirichlet series and systems of dilated functions in $L^2(0,1)$

  title={A Hilbert space of Dirichlet series and systems of dilated functions in \$L^2(0,1)\$},
  author={H̊akan Hedenmalm and Peter Lindqvist and Kristian Seip},
  journal={Duke Mathematical Journal},
For a function $\varphi$ in $L^2(0,1)$, extended to the whole real line as an odd periodic function of period 2, we ask when the collection of dilates $\varphi(nx)$, $n=1,2,3,\ldots$, constitutes a Riesz basis or a complete sequence in $L^2(0,1)$. The problem translates into a question concerning multipliers and cyclic vectors in the Hilbert space $\cal H$ of Dirichlet series $f(s)=\sum_n a_nn^{-s}$, where the coefficients $a_n$ are square summable. It proves useful to model $\cal H$ as the $H… 
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