On the shift semigroup on the Hardy space of Dirichlet series (Q625981)

We 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 \(\mathfrak{R}(s) >\frac{1}{2}\). 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 \( \varphi\mathcal{H}^{2}\) for some \(\mathcal{H}^{2}\)-inner function \(\varphi \).