Geodesic
Best approximations by rational vector-valued functions in Hardy spaces
Sbornik. Mathematics, Tome 61 (1988) no. 1, pp. 137-145 
S. A. Ivanov. Best approximations by rational vector-valued functions in Hardy spaces. Sbornik. Mathematics, Tome 61 (1988) no. 1, pp. 137-145. http://geodesic.mathdoc.fr/item/SM_1988_61_1_a9/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Interpolation conditions satisfied by a best norm approximation among all rational functions of total order $N$ are obtained for vector-valued functions in the Hardy space $H^2(E)$. Also, descriptions are given for bases in finite-dimensional subspaces invariant under the backward shift operator. Bibliography: 9 titles.

[1] Uolsh D. L., Interpolyatsiya i approksimatsiya ratsionalnymi funktsiyami v kompleksnoi oblasti, Nauka, M., 1961 | MR

[2] Baker G. A., Essentials of Padé approximants, N.Y.–San Franc., 1975 | MR

[3] Erokhin V., “O nailuchshem priblizhenii analiticheskikh funktsii postroeniem ratsionalnykh drobei so svobodnymi polyusami”, DAN SSSR, 128:1 (1959), 29–33

[4] Levin A. L., Tikhomirov V. M., “O priblizheniyakh analiticheskikh funktsii ratsionalnymi”, DAN SSSR, 174:2 (1967), 279–282 | MR | Zbl

[5] Pekarskii A. A., “Klassy analiticheskikh funktsii, opredelyaemye nailuchshimi ratsionalnymi priblizheniyami v $H_p$”, Matem. sb., 127(169) (1985), 3–20 | MR | Zbl

[6] Nikolskii N. K., Lektsii ob operatore sdviga, Nauka, M., 1980 | MR

[7] Nikolskii N. K., Pavlov B. S., “Bazisy iz sobstvennykh vektorov vpolne neunitarnykh szhatii i kharakteristicheskaya funktsiya”, Izv. AN SSSR. Ser. matem., 34:1 (1970), 90–133 | MR | Zbl

[8] Ivanov S. A., “Bazisy iz ratsionalnykh vektor-funktsii i mnozhestva Karlesona”, DAN ArmSSR, 80:1 (1985), 20–23 | MR

[9] Vasyunin V. I., “Bezuslovno skhodyaschiesya spektralnye razlozheniya zadachi interpolyatsii”, Tr. MIAN, 1977, 5–49 | MR