Geodesic
On the~best local nonglobal rational approximation in the~space~$H_2$
Fundamentalʹnaâ i prikladnaâ matematika, Tome 4 (1998) no. 4, pp. 1423-1426

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For any natural number $k$ the function from the Hardy space $H_2$ is found that its rational approximation of $(k,1)$ degree with pole in $1/\sqrt{2}$ gives the best local nonglobal approximation in the set of all rational functions of $(k,1)$ degree. 
@article{FPM_1998_4_4_a18,
     author = {M. A. Nazarenko},
     title = {On the~best local nonglobal rational approximation in the~space~$H_2$},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {1423--1426},
     publisher = {mathdoc},
     volume = {4},
     number = {4},
     year = {1998},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1998_4_4_a18/}
}
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M. A. Nazarenko. On the~best local nonglobal rational approximation in the~space~$H_2$. Fundamentalʹnaâ i prikladnaâ matematika, Tome 4 (1998) no. 4, pp. 1423-1426. http://geodesic.mathdoc.fr/item/FPM_1998_4_4_a18/