Abstract
It is proved that the sums \( \sum_{k=1}^{n} \frac{1}{(z-a_{k})^{2}}\mspace{2mu}, \qquad \operatorname{Im}a_{k} < 0, \quad n \in \mathbb{N}, \) 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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Acknowledgments
The author wishes to express gratitude to P. A. Borodin for posing the problem and useful advice during the work on the paper, as well as to O. N. Kosukhin for useful remarks.
Funding
This work was supported by the Russian Foundation for Basic Research under grant 18-01-00333a.
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Dyuzhina, N.A. Density of Derivatives of Simple Partial Fractions in Hardy Spaces in the Half-Plane. Math Notes 109, 46–53 (2021). https://doi.org/10.1134/S0001434621010065
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DOI: https://doi.org/10.1134/S0001434621010065