Geodesic
Integral representations and best approximation by generalized polynomials in systems of Mittag-Leffler type
Izvestiya. Mathematics, Tome 23 (1984) no. 3, pp. 449-471 
M. M. Dzhrbashyan; V. M. Martirosyan. Integral representations and best approximation by generalized polynomials in systems of Mittag-Leffler type. Izvestiya. Mathematics, Tome 23 (1984) no. 3, pp. 449-471. http://geodesic.mathdoc.fr/item/IM2_1984_23_3_a2/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Integral representations are established for generalized polynomials in certain systems of functions of Mittag-Leffler type, and a theorem is proved on the analytic continuation of functions with a sufficiently high degree of approximation by such polynomials. Bibliography: 15 titles.

[1] Dzhrbashyan M. M., “O zamknutosti sistemy tipa Mittag-Lefflera”, Dokl. AN SSSR, 219:6 (1974), 1302–1305 | Zbl

[2] Dzhrbashyan M. M., Integralnye preobrazovaniya i predstavleniya funktsii v kompleksnoi oblasti, Nauka, M., 1966

[3] Viner N., Peli R., Preobrazovanie Fure v kompleksnoi oblasti, Nauka, M., 1964 | MR

[4] Dzhrbashyan M. M., “O popolnenii i zamykanii nepolnoi sistemy funktsii $\{e^{-\mu k^x}x^{s_{k^{-1}}}\}_1^\infty$”, Dokl. AN SSSR, 141:3 (1961), 539–542 | Zbl

[5] Dzhrbashyan M. M., “Kharakteristika zamknutykh lineinykh obolochek dvukh semeistv nepolnykh sistem analiticheskikh funktsii”, Matem. sb., 114(156):1 (1981), 3–84 | MR | Zbl

[6] Dzhrbashyan M. M., Nersesyan A. B., “O postroenii nekotorykh spetsialnykh biortogonalnykh sistem”, Izv. AN ArmSSR, Matematika, XII:5 (1959), 17–42

[7] Dzhrbashyan M. M., Nersesyan A. B., “Razlozheniya po nekotorym biortogonalnym sistemam i kraevye zadachi dlya differentsialnogo uravneniya drobnogo poryadka”, Tr. Mosk. matem. ob-va, X, 1961, 89–179

[8] Dzhrbashyan M. M., “Teoremy edinstvennosti analiticheskikh funktsii, asimptoticheski predstavimykh ryadami Dirikhle–Teilora”, Matem. sb., 91(133):4(8) (1973), 580–626 | MR | Zbl

[9] Dzhrbashyan M. M., “Bazisnost nekotorykh biortogonalnykh sistem i reshenie kratnoi interpolyatsionnoi zadachi v klassakh $H^p$ v poluploskosti”, Dokl. AN SSSR, 234:3 (1977), 517–520 ; Р�Р·РІ. РђРќ РЎРЎРЎР . РЎРμСЂ. матРμРј., 42:6 (1978), 1322–1384 | MR | Zbl | MR | Zbl

[10] Dzhrbashyan M. M., “Ob integralnom predstavlenii i edinstvennosti nekotorykh klassov tselykh funktsii”, Dokl. AN SSSR, 85:1 (1952), 29–32 | Zbl

[11] Dzhrbashyan M. M., “Ob odnom novom integralnom preobrazovanii i ego primenenii v teorii tselykh funktsii”, Dokl. AN SSSR, 95 (1954), 1133–1136 ; Р�Р·РІ. РђРќ РЎРЎРЎР . РЎРμСЂ. матРμРј., 19:2 (1955), 133–190 | Zbl | MR | Zbl

[12] Musoyan V. X., “Analiticheskoe prodolzhenie funktsii, approksimiruemykh polnoi sistemoi Dirikhle”, Dokl. AN ArmSSR, LXXII:3 (1981), 135–140 | MR

[13] Dzhrbashyan M. M., Avetisyan A. E., “Integralnye predstavleniya nekotorykh klassov funktsii, analiticheskikh v oblasti ugla”, Dokl. AN SSSR, 120:3 (1958), 457–460 ; РЎРёР±РёСЂСЃРє. матРμРј. Р¶., 1:3 (1960), 383–426 | Zbl | MR | Zbl

[14] Gofman K., Banakhovy prostranstva analiticheskikh funktsii, IL, M., 1963

[15] Martirosyan V. M., “Zamykanie i bazisnost nekotorykh biortogonalnykh sistem i reshenie kratnoi interpolyatsionnoi zadachi v uglovykh oblastyakh”, Izv. AN ArmSSR, Matematika, XIII:5,6 (1978), 490–531 | MR