Geodesic
Biorthogonal systems of rational functions and best approximation of the Cauchy kernel on the real axis
Sbornik. Mathematics, Tome 24 (1974) no. 3, pp. 409-433 
M. M. Dzhrbashyan. Biorthogonal systems of rational functions and best approximation of the Cauchy kernel on the real axis. Sbornik. Mathematics, Tome 24 (1974) no. 3, pp. 409-433. http://geodesic.mathdoc.fr/item/SM_1974_24_3_a4/
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     title = {Biorthogonal systems of rational functions and best approximation of the {Cauchy} kernel on the real axis},
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Voir la notice de l'article provenant de la source Math-Net.Ru

This paper is devoted to problems of the representation and best approximation of the Cauchy kernel on the whole real axis $-\infty. The method proposed here for the solution of such problems is based on the attraction of systems of rational functions with fixed poles which are orthogonal or biorthogonal on the whole axis. Bibliography: 9 titles.

[1] N. I. Akhiezer, “O vzveshennom priblizhenii nepreryvnykh funktsii mnogochlenami na vsei chislovoi osi”, Uspekhi matem. nauk, XI:4 (70) (1956), 3–43 | MR

[2] N. I. Akhiezer, Lektsii po teorii approksimatsii, izd-vo «Nauka», Moskva, 1966

[3] G. Wahde, “An extremal problem related to Bernstein's approximation problem”, Math. Scand., 15 (1964), 131–141 | MR | Zbl

[4] F. Malmquist, “Sur la d une classe de fonctions analytiques par leurs valeurs dans un ensamble donne de points”, Comptes rendus sixieme congris (1925) des math. scand., Kopenhagen, 1926, 253–259 | Zbl

[5] S. Takenaka, “On the orthogonal functions and a new formula of interpolation”, Japan. J. Math., 2 (1925), 129–145

[6] Dzh. Uolsh, Interpolyatsiya i approksimatsiya ratsionalnymi funktsiyami v kompleksnoi oblasti, IL, Moskva, 1961 | MR

[7] M. M. Dzhrbashyan, “K teorii ryadov Fure po ratsionalnym funktsiyam”, Izv. AN Arm. SSR, seriya fiz.-matem., estestv. i tekhn. nauk, 9:7 (1956), 3–28 | MR

[8] E. Titchmarsh, Vvedenie v teoriyu integralov Fure, OGIZ, Moskva, 1948

[9] M. M. Dzhrbashyan, Integralnye preobrazovaniya i predstavleniya funktsii v kompleksnoi oblasti, izd-vo «Nauka», Moskva, 1966