Geodesic
Density of Derivatives of Simple Partial Fractions in Hardy Spaces in the Half-Plane
Matematičeskie zametki, Tome 109 (2021) no. 1, pp. 57-66

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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 $H_{p}$, $1$, 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.
Keywords: approximation, density, Hardy spaces.
Mots-clés : simple partial fractions 
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     author = {N. A. Dyuzhina},
     title = {Density of {Derivatives} of {Simple} {Partial} {Fractions} in {Hardy} {Spaces} in the {Half-Plane}},
     journal = {Matemati\v{c}eskie zametki},
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     publisher = {mathdoc},
     volume = {109},
     number = {1},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2021_109_1_a5/}
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N. A. Dyuzhina. Density of Derivatives of Simple Partial Fractions in Hardy Spaces in the Half-Plane. Matematičeskie zametki, Tome 109 (2021) no. 1, pp. 57-66. http://geodesic.mathdoc.fr/item/MZM_2021_109_1_a5/