Abstract:
It is proved that the sums
$$
\sum_{k=1}^{n} \frac{1}{(z-a_{k})^{2}}, \qquad \operatorname{Im}a_{k} < 0, \quad n \in \mathbb{N},
$$
are dense in all Hardy spaces $H_{p}$, $1<p< \infty$, in the upper half-plane and in the space of functions analytic in the upper half-plane, continuous in its closure, and tending to zero at infinity.
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