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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] P. A. Borodin, S. V. Konyagin, “Convergence to zero of exponential sums with positive integer coefficients and approximation by sums of shifts of a single function on the line”, Anal. Math., 44:2 (2018), 163–183 | DOI | MR | Zbl

[2] N. A. Dyuzhina, “Plotnost summ sdvigov odnoi funktsii v prostranstvakh Khardi v poluploskosti”, Matem. zametki, 106:5 (2019), 669–678 | DOI | Zbl

[3] V. I. Danchenko, “Otsenki rasstoyanii ot polyusov logarifmicheskikh proizvodnykh mnogochlenov do pryamykh i okruzhnostei”, Matem. sb., 185:8 (1994), 63–80 | MR | Zbl

[4] P. A. Borodin, O. N. Kosukhin, “O priblizhenii naiprosteishimi drobyami na deistvitelnoi osi”, Vestn. Mosk. un-ta. Ser. 1. Matem., mekh., 2005, no. 1, 3–8 | MR | Zbl

[5] P. Kusis, Vvedenie v teoriyu prostranstv $H^p$ s prilozheniem dokazatelstva Volffa teoremy o korone, Mir, M., 1984 | MR | Zbl

[6] Dzh. Garnett, Ogranichennye analiticheskie funktsii, Mir, M., 1984 | MR | Zbl

[7] P. A. Borodin, “Plotnost polugruppy v banakhovom prostranstve”, Izv. RAN. Ser. matem., 78:6 (2014), 21–48 | DOI | MR | Zbl

[8] V. I. Danchenko, M. A. Komarov, P. V. Chunaev, “Ekstremalnye i approksimativnye svoistva naiprosteishikh drobei”, Izv. vuzov. Matem., 2018, no. 12, 9–49 | Zbl