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@article{INTO_2018_153_a2, author = {A. V. Bratishchev}, title = {On {Gelfond--Leontiev} {Operators} of {Generalized} {Differentiation}}, journal = {Itogi nauki i tehniki. Sovremenna\^a matematika i e\"e prilo\v{z}eni\^a. Temati\v{c}eskie obzory}, pages = {29--54}, publisher = {mathdoc}, volume = {153}, year = {2018}, language = {ru}, url = {http://geodesic.mathdoc.fr/item/INTO_2018_153_a2/} }
TY - JOUR AU - A. V. Bratishchev TI - On Gelfond--Leontiev Operators of Generalized Differentiation JO - Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory PY - 2018 SP - 29 EP - 54 VL - 153 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/INTO_2018_153_a2/ LA - ru ID - INTO_2018_153_a2 ER -
%0 Journal Article %A A. V. Bratishchev %T On Gelfond--Leontiev Operators of Generalized Differentiation %J Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory %D 2018 %P 29-54 %V 153 %I mathdoc %U http://geodesic.mathdoc.fr/item/INTO_2018_153_a2/ %G ru %F INTO_2018_153_a2
A. V. Bratishchev. On Gelfond--Leontiev Operators of Generalized Differentiation. Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Complex analysis, Tome 153 (2018), pp. 29-54. http://geodesic.mathdoc.fr/item/INTO_2018_153_a2/
[1] Bratischev A. V., Bazisy Kete, tselye funktsii i ikh prilozheniya, Diss. na soiskanie uch. step. dokt. fiz.-mat. nauk, RGU, Rostov-na-Donu, 1993
[2] Bratischev A. V., “O lineinykh operatorakh, simvol kotorykh yavlyaetsya funktsiei proizvedeniya svoikh argumentov”, Dokl. RAN, 365:1 (1999), 9–12 | MR
[3] Bratischev A. V., “Opisanie obobschennykh preobrazovanii Borelya, sokhranyayuschikh teoremu Poiya”, Vestn. DGTU, 1:1 (2001), 79–89
[4] Bratischev A. V., “Oblast skhodimosti ryada obobschennykh eksponent, obrazovannogo tseloi funktsiei konechnogo poryadka”, Vestn. DGTU, 3:2 (2003), 139–144
[5] Bratischev A. V., “Operator obobschennogo differentsirovaniya, porozhdennyi funktsiei Geine”, Sovremennye problemy teorii funktsii i ikh prilozheniya, Tez. dokl. 13 Saratovskoi zimnei mat. shkoly, Nauchnaya kniga, Saratov, 2006, 36–37
[6] Bratischev A. V., “Khaotichnost kommutiruyuschikh s differentsirovaniem Dankla preobrazovanii prostranstv analiticheskikh funktsii”, Vestn. DGTU, 9:2 (2009), 196–207
[7] Bratischev A. V., “Operatory obobschennogo differentsirovaniya Gelfonda—Leonteva i polinomy Brenke”, Vestn. DGTU, 10:6 (2010), 813–824
[8] Bratischev A. V., “O predstavlenii lineinykh operatorov, kommutiruyuschikh s differentsirovaniem, v odnosvyaznoi oblasti”, Vestn. DGTU, 14:1 (2014), 15–21
[9] Bratischev A. V., “O predstavlenii operatora obobschennogo differentsirovaniya Gelfonda—Leonteva v odnosvyaznoi oblasti”, Vestn. DGTU, 14:2 (2014), 21–26
[10] Bratischev A. V., Matematicheskaya teoriya upravlyaemykh dinamicheskikh sistem. Vvedenie v ponyatiya i metody, Uch. posobie, Izdatelskii tsentr DGTU, Rostov-na-Donu, 2015
[11] Bratischev A. V., “Ob operatore obobschennogo differentsirovaniya Gelfonda—Leonteva”, Mezhdunar. mat. konf. po teorii funktsii, posvyaschennaya 100-letiyu chl.-korr. AN SSSR A. F. Leonteva (Ufa, 24–27 maya 2017 g, Tez. dokl.), RITs BashGU, Ufa, 2017, 29–30
[12] Bratischev A. V., Kalinichenko L. I., “Opisanie oblasti skhodimosti ryada obobschennykh eksponent”, Dokl. RAN, 331:6 (1993), 666–667
[13] Bratischev A. V., Kalinichenko L. I., “Kriterii $s$-invariantnosti oblasti skhodimosti ryada obobschennykh eksponent”, Kompleksnyi analiz, differentsialnye uravneniya, chislennye metody i prilozheniya, v. 1, Kompleksnyi analiz, Inst. mat. s VTs RAN, Ufa, 1996, 16–22
[14] Bratischev A. V., Korobeinik Yu. F., “Obschii vid lineinykh operatorov, perestanovochnykh s operatsiei differentsirovaniya”, Mat. zametki, 12:2 (1972), 187–195 | MR
[15] Bratischev A. V., Morzhakov A. V., “O multiplikatore pary mnozhestv kompleksnoi ploskosti”, Vestn. DGTU, 4:3 (2004), 270–281
[16] Bratischev A. V., Morzhakov A. V., “Predstavlenie operatora obobschennogo differentsirovaniya v odnom klasse odnosvyaznykh oblastei”, Vestn. DGTU, 5:4 (2005), 481–490
[17] Bratischev A. V., Morzhakov A. V., “O rezolvente odnogo klassa operatorov obobschennogo diferentsirovaniya”, Vestn. DGTU, 6:2 (2006), 85–88
[18] Bratischev A. V., Morzhakov A. V., “Ob odnodiagonalnykh operatorakh”, Integro-differentsialnye operatory i ikh prilozheniya, Izd-vo DGTU, Rostov-na-Donu, 2008 \ischllvol 8, 196–207
[19] Gelfond A. O., “Lineinye differentsialnye uravneniya s postoyannymi koeffitsientami beskonechnogo poryadka i asimptoticheskie periody tselykh funktsii”, Tr. mat. in-ta im. V. A. Steklova, 38 (1951), 42–67 | Zbl
[20] Gelfond A. O., Ischislenie konechnykh raznostei, Nauka, M., 1967 | MR
[21] Gelfond A. O., Leontev A. F., “Ob odnom obobschenii ryada Fure”, Mat. sb., 29 (71):3 (1951), 477–500 | MR | Zbl
[22] Goldberg A. A., Levin B. Ya., Ostrovskii I. V., “Tselye i meromorfnye funktsii”, Itogi nauki i tekhn., Sovrem. probl. mat. Fundam. napravleniya, 85, VINITI, M., 1990, 5–186
[23] Epifanov O. V., “Kriterii epimorfnosti svertki v proizvolnykh oblastyakh kompleksnoi ploskosti”, Mat. zametki, 31:5 (1982), 695–705 | MR | Zbl
[24] Epifanov O. V., Operatory svertki i differentsialnye operatory beskonechnogo poryadka v prostranstvakh analiticheskikh funktsii, Diss. na soiskanie uch. step. dokt. fiz.-mat. nauk, In-t mat., Kiev, 1990
[25] Ivanova O. A., Melikhov S. N., “Ob interpoliruyuschei funktsii A. N. Leonteva”, Ufim. mat. zh., 6:3 (2014), 17–27 | MR
[26] Karamov I. I., Napalkov V. V., “Obobschennyi operator Dankla”, Ufim. mat. zh., 6:1 (2014), 59–68 | MR
[27] byКим В. Э. “Gipertsiklichnost i khaotichnost operatorov obobschennoi svertki, porozhdaemykh operatorami Gelfonda—Leonteva”, Mat. sb., 85:6 (2009), 849–856 | Zbl
[28] Korobeinik Yu. F., “Ob operatorakh obobschennogo differentsirovaniya, primenimykh k lyuboi analiticheskoi funktsii”, Izv. AN SSSR. Ser. mat., 28:4 (1964), 833–854 | Zbl
[29] Korobeinik Yu. F., “Lineinye operatory, perestanovochnye s differentsirovaniem i opredelennye v prostranstve funktsii, analiticheskikh v beskonechnykh oblastyakh”, Vyssh. tekhn. uch. zaved. Mat., v. 9, 1973, 35–44
[30] Korobeinik Yu. F., “Predstavlyayuschie sistemy”, Izv. AN SSSR. Ser. mat., 42:2 (1978), 325–355 | MR
[31] Korobeinik Yu. F., O razreshimosti v kompleksnoi oblasti nekotorykh obschikh klassov lineinykh operatornykh uravnenii, TsVVR, Rostov-na-Donu, 2005
[32] Korobeinik Yu. F., Donskov Yu. M., “Analiticheskie resheniya uravneniya Eilera beskonechnogo poryadka”, Izv. vuzov. Mat., 11 (90) (1969), 46–52
[33] Levin B. Ya., Raspredelenie kornei tselykh funktsii, GITTL, M., 1956
[34] Leontev A. F., “Ryady polinomov Dirikhle i ikh obobscheniya”, Tr. mat. in-ta im. V. A. Steklova, 39 (1951), 1–216 | MR
[35] Leontev A. F., “Ob oblasti regulyarnosti predelnoi funktsii odnoi posledovatelnosti analiticheskikh funktsii”, Mat. sb., 39:4 (1956), 405–422 | Zbl
[36] Leontev A. F., Obobschennye ryady eksponent, Nauka, M., 1981 | MR
[37] Leontev A. F., “Predstavlenie funktsii v vypuklykh oblastyakh obobschennymi ryadami eksponent”, Acta Sci. Math. Szeged., 45 (1983), 305–315 | Zbl
[38] Leontev A. F., “Oblast skhodimosti ryada obobschennykh eksponent”, Mat. sb., 123:1 (1984), 3–10 | MR
[39] Leontev A. F., “K voprosu o predstavlenii funktsii ryadami obobschennykh eksponent”, Anal. Math., 12 (1986), 213–228 | DOI | Zbl
[40] Leontev A. F., “Predstavlenie funktsii ryadami obobschennykh eksponent”, Mat. sb., 134:4 (1987), 496–510 | Zbl
[41] Leonteva T. A., “O vypuklosti oblasti skhodimosti ryada obobschennykh eksponent”, Vestn. MGU. Ser. 1. Mat., mekh., 5 (1990), 28–32 | MR | Zbl
[42] Linchuk S. S., “Diagonalnye operatory v prostranstvakh analiticheskikh funktsii i ikh prilozheniya”, Aktualnye voprosy teorii funktsii, Izd-vo Rostov. un-ta, Rostov-na-Donu, 1987, 118–121 | MR
[43] Lunts G. L., “O nekotorykh obobscheniyakh ryadov Dirikhle”, Mat. sb., 10:1-2 (1942), 33–50
[44] Lunts G. L., “O skhodimosti nekotorykh obschikh ryadov v prostranstvakh neskolkikh kompleksnykh peremennykh”, Sib. mat. zh., 13:2 (1972), 467–472
[45] Mavrodi N. N., “Neobkhodimye i dostatochnye usloviya analiticheskoi prodolzhimosti stepennogo ryada”, Aktualnye problemy matematicheskogo analiza, Izd-vo GinGo, Rostov-na-Donu, 2000, 94–99
[46] Morzhakov A. V., “Opisanie klassa operatorov obobschennogo differentsirovaniya v prostranstve analiticheskikh funktsii”, Tr. VIII Mezhdunar. nauch.-tekhn. konf. po dinamike tekhnologicheskikh sistem, Izdatelskii tsentr DGTU, Rostov-na-Donu, 2007, 189–193
[47] Morzhakov A. V., Issledovanie operatorov i operatornykh uravnenii, porozhdennykh obobschennym differentsirovaniem, Diss. na soiskanie uch. step. kand. fiz.-mat. nauk, DGTU, Rostov-na-Donu, 2008
[48] Morzhakov A. V., Melikhov S. N., “Predstavlenie operatora obobschennogo differentsirovaniya v odnom klasse zvezdnykh oblastei”, Teoriya funktsii, ee prilozheniya i smezhnye voprosy, Mat. 7 Kazan. letnei nauch. shkoly-konf., Izd-vo KGU, Kazan, 2005, 112–113
[49] Napalkov V. V., “O rasshirenii operatora obobschennogo differentsirovaniya”, Mat. zametki, 6:4 (1969), 425–436 | MR | Zbl
[50] Pugachev V. S., Osnovy avtomaticheskogo upravleniya, Nauka, M., 1974
[51] Samko S. G., Kilbas A. A., Marichev O. I., Integraly i proizvodnye drobnogo poryadka i nekotorye ikh prilozheniya, Nauka i tekhnika, Minsk, 1987
[52] Smirnov V. I., Lebedev N. A., Konstruktivnaya teoriya funktsii kompleksnogo peremennogo, Nauka, M., 1964
[53] Khaplanov M. G., “Lineinye preobrazovaniya analiticheskikh prostranstv”, Dokl. AN SSSR, 80:1 (1951), 21–24 | MR | Zbl
[54] Tsarkov Yu. M., “Izomorfizmy nekotorykh analiticheskikh prostranstv, perestanovochnykh so stepenyu operatora differentsirovaniya”, Teoriya funktsii, funktsionalnyi analiz i ikh prilozheniya, v. 11, 1970, 86–92 | Zbl
[55] Agmon S., “On the singularities of Taylor series with reciprocal coefficients”, Pac. J. Math., 2 (1952), 431–453 | DOI | MR | Zbl
[56] Bateman H., Erdelyi A., Higher transcendental function, v. 1, Mc Grow-Hill, New York–Toronto–London, 1953
[57] Betancor J. J., Sifi M., Trimeche K., “Hypercyclic and chaotic convolution operators associated with the Dunkl operator on $\mathbb{C}$”, Acta Math. Hung., 106:1-2 (2005), 101–116 | DOI | MR | Zbl
[58] Bieberbach L., Analitischer Fortssetzung, Springer-Verlag, Berlin–Göttingen–Heidelberg, 1955 | MR
[59] Boas R. P., Buck R. C., Polynomial expansions of analytic functions, Springer-Verlag, Berlin–Göttingen–Heidelberg, 1958 | MR | Zbl
[60] Brenke W. C., “On generating functions of polynomial systems”, Am. Math. Month, 52 (1945), 297–301 | DOI | MR | Zbl
[61] Davis H. T., “The Euler differential equation of infinite order”, Am. Math. Month, 32 (1925), 223–233 | DOI | MR | Zbl
[62] Dickson D. G., “Analytic mean periodic functions”, Trans. Am. Math. Soc., 110 (1964), 361–374 | DOI | MR | Zbl
[63] Gelfond A., “Sur les systemes complets de fonctions analytiques”, Mat. sb., 4 (46):1 (1938), 149–156
[64] Köthe G., “Dualität in der Funktionentheorie”, J. Reine Angew. Math., 191 (1953), 30–49 | MR | Zbl
[65] Schottlaender S., “Der Hadamardsche Multiplikationssatz und weitere Kompositionssätze der Funktiontheorie”, Math. Nachr., 11:4/5 (1954), 239–294 | DOI | MR | Zbl