01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
4.11.1958
E-mail:
Keywords:
invariant subspace, syntheses, differential operator, root elements, systems of the operators, duality theorem, submodule of the entire functions,
entire function, zero order.
UDC:
517.5, 517
Subject:
Spectral syntheses in complex area.
Local description of the entire functions.
Approximation of the entire functions.
Main publications:
Chebyshevskie tsentry i κ-normalnye prostranstva // Mat. zametki. 1981. T. 29, # 5. S. 659–672 (sovmestno s V. N. Zamyatinym).
Spektralnyi sintez operatora kratnogo differentsirovaniya // Dokl. AN SSSR. 1989. T. 307, # 1. S. 24–27 (sovmestno s I. F. Krasichkovym-Ternovskim).
Lokalnoe opisanie zamknutykh podmodulei v spetsialnom module tselykh funktsii eksponentsialnogo tipa // Mat. zametki. 1989. T. 46, # 6. S. 94–100.
Spektralnyi sintez dlya operatora, porozhdaemogo umnozheniem na stepen nezavisimoi peremennoi // Mat. sb. 1991. T. 182, # 6. S. 828–848.
Spektralnyi sintez dlya sistem differentsialnykh operatorov s postoyannymi koeffitsientami // DAN RAN, 355. # 1, 1997. S. 28–30.
Spektralnyi sintez dlya sistem differentsialnykh operatorov s postoyannymi koeffitsientami. Teorema dvoistvennosti // Matem. sb. 1998. T. 189. # 9. S. 143–160.
Lokalnoe opisanie zamknutykh podmodulei v spetsialnom module tselykh funktsii eksponentsialnogo tipa // Matem. sb. 2001. T. 192. # 11. S. 35–54 (sovmestno s I. F. Krasichkovym-Ternovskim).
Spektralnyi sintez dlya sistem differentsialnykh operatorov s postoyannymi koeffitsientami // Matem. sb. 2003. T. 194. # 12. S. 123–160.
Proektivnoe i in'ektivnoe opisaniya v kompleksnoi oblasti. Spektralnyi sintez i lokalnoe opisanie v kompleksnoi oblasti
/ Slavyansk-na-Kubani : Izdatelskii tsentr KubGU, 2013. - 304 s.
Yu. S. Saranchuk, A. B. Shishkin, “General elementary solution of a homogeneous $q$-sided convolution type equation”, St. Petersburg Math. J., 34:4 (2023), 695–713
2.
A. A. Tatarkin, A. B. Shishkin, “Exponential synthesis in the kernel of a $q$-sided convolution operator”, Investigations on linear operators and function theory. Part 50, Zap. Nauchn. Sem. POMI, 512, POMI, St. Petersburg, 2022, 191–222
3.
A. B. Shishkin, “On continuous endomorphisms of entire functions”, Sb. Math., 212:4 (2021), 567–591
4.
A. A. Tatarkin, A. B. Shishkin, “Synthesis in the kernel of the three-way convolution operator”, Proceedings of the Voronezh spring mathematical school
“Modern methods of the theory of boundary-value problems. Pontryagin
readings – XXX”.
Voronezh, May 3-9, 2019. Part 4, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 193, VINITI, Moscow, 2021, 130–141
5.
A. B. Shishkin, “One-sided dual schemes”, Vladikavkaz. Mat. Zh., 22:3 (2020), 124–150
6.
A. B. Shishkin, A. N. Chernyshev, R. G. Pismennyi, “Approksimatsionnaya teorema dlya odnorodnogo uravneniya
simmetrichnoi svertki”, Sbornik nauchnykh trudov regionalnoi nauchno-prakticheskoi konferentsii, Pedagogicheskii vuz v sotsiokulturnom i obrazovatelnom prostranstve regiona, v dvukh chastyakh. Chast 1 (g. Slavyansk-na-Kubani, 27–29 sentyabrya 2019 goda), 2019, 256–262
7.
A. B. Shishkin, “Symmetric representations of holomorphic functions”, Probl. anal. Issues Anal., 7(25):2 (2018), 124–136
A. B. Shishkin, “Algebraicheskoe orientirovanie mnozhestv. IV. Teorema Stoksa”, Vestnik AGU, seriya «Estestvenno-matematicheskie i tekhnicheskie nauki», 2018, no. 1(216), 22–33
9.
A. B. Shishkin, “Algebraicheskoe orientirovanie mnozhestv. III. Integral po proektsii”, Vestnik AGU, seriya «Estestvenno-matematicheskie i tekhnicheskie nauki», 2017, no. 2(201), 14–24
10.
A. B. Shishkin, “Factorization of entire symmetrical functions of exponential type”, Izv. Saratov Univ. (N.S.), Ser. Math. Mech. Inform., 16:1 (2016), 42–68
11.
A. B. Shishkin, “Exponential synthesis in the kernel of a symmetric convolution”, J. Math. Sci. (N. Y.), 229:5 (2018), 572–599
12.
A. B. Shishkin, “Algebraicheskoe orientirovanie mnozhestv. I. Simpleksirovanie”, Vestnik Adygeiskogo gosudarstvennogo universiteta, seriya «Estestvenno-matematicheskie i tekhnicheskie», 2016, no. 3(186), 28–38
13.
A. B. Shishkin, “Algebraicheskoe orientirovanie mnozhestv. II. Mera po proektsii”, Vestnik Adygeiskogo gosudarstvennogo universiteta, seriya «Estestvenno-matematicheskie i tekhnicheskie», 2016, no. 4(191), 28–42
14.
A. B. Shishkin, R. G. Pismennyiy, “Axiomatic Determination Of Elementary Multi-Valued Functions For A Complex Variable”, International Journal of Applied Engineering Research (IJAER), 10(3) (2015), 6467–6477
15.
A. B. Shishkin, “Projective and injective descriptions in the complex domain. Duality”, Izv. Saratov. Univ. Mat. Mekh. Inform., 14:1 (2014), 47–65
16.
T. A. Volkovaya, A. B. Shishkin, “Local description of entire functions. Submodules of rank 1”, Vladikavkaz. Mat. Zh., 16:2 (2014), 14–28
17.
T. A. Volkovaya, A. B. Shishkin, “Lokalnoe opisanie tselykh funktsii”, Matematicheskii forum. Issledovaniya po matematicheskomu analizu, 6:1 (2014), 215–226 (to appear)
18.
A. B. Shishkin, Proektivnoe i in'ektivnoe opisaniya v kompleksnoi oblasti., Spektralnyi sintez i lokalnoe opisanie analiticheskikh funktsii., Izdatelskii tsentr “KubGU”, Slavyansk-na-Kubani, 2013 , 304 pp. \href{http://www.sgpi.ru/userfiles/Proektivnoe i in'ektivnoe opisaniya v kompleksnoi oblasti.pdf}
19.
A. B. Shishkin, “Integrirovanie na orientirovannom mnozhestve po proektsii”, Vestnik Adygeiskogo gosudarstvennogo universiteta. Seriya 4: Estestvenno-matematicheskie i tekhnicheskie nauki, 2012, no. 1, 15–23
20.
A. B. Shishkin, “Orientirovanie mnozhestv”, Trudy FORA, 2011, no. 16, 27–31
21.
A. B. Shishkin, Proektivnoe i in'ektivnoe opisaniya v kompleksnoi oblasti, LAMBERT Academic Publishing GmbH & Co. KG, Saarbrucken, Germany, 2011 , 309 pp.
22.
R. G. Pismennyi, A. B. Shishkin, “Rasscheplenie tselykh funktsii konechnogo poryadka na ekvivalentnye mnozhiteli”, Vestnik Adygeiskogo gosudarstvennogo universiteta, 2010, no. 2(61), 23–28
23.
A. B. Shishkin, “Obilnost glavnykh $\mathbf{C}[\pi]$-podmodulei”, Izvestiya vysshikh uchebnykh zavedenii severo-kavkazskii region. Estestvennye nauki, 2009, no. 3, 34–38
24.
A. B. Shishkin, “Sravnenie tselykh funktsii s blizkimi nulyami”, Trudy FORA, 2007, no. 12, 8–17
25.
A. B. Shishkin, “Spectral synthesis for systems of differential operators with constant coefficients”, Sb. Math., 194:12 (2003), 1865–1898
26.
I. F. Krasichkov-Ternovskii, A. B. Shishkin, “Local description of closed submodules of a special module of entire functions of exponential type”, Sb. Math., 192:11 (2001), 1621–1638
27.
A. B. Shishkin, “Spectral synthesis for systems of differential operators with constant coefficients. Duality theorem”, Sb. Math., 189:9 (1998), 1423–1440
28.
A. B. Shishkin, Spektralnyi sintez i lokalnoe opisanie analiticheskikh funktsii, Izdatelskii tsentr AGPI, Armavir, 1995 , 192 pp.
29.
A. B. Shishkin, “Spectral synthesis for an operator generated by multiplication by a power of the independent variable”, Math. USSR-Sb., 73:1 (1992), 211–229
30.
A. B. Shishkin, “Local description of closed submodules in a special module of entire functions of exponential type”, Math. Notes, 46:6 (1989), 952–956
31.
I. F. Krasichkov-Ternovskii, A. B. Shishkin, “Spectral synthesis for the multiple differentiation operator”, Dokl. Math., 40:1 (1990), 16–19
32.
V. N. Zamyatin, A. B. Shishkin, “Chebyshev centers and $\varkappa$-normal spaces”, Math. Notes, 29:5 (1981), 336–342
33.
A. B. Shishkin, Teoriya funktsii kompleksnoi peremennoi, Rekomendovano UMO po spetsialnostyam pedagogicheskogo obrazovaniya v kachestve uchebnogo posobiya dlya studentov vysshikh uchebnykh zavedenii, obuchayuschikhsya po spetsialnosti 050201.65 - matematika (Reshenie UMO MO RF #1 ot 09.02.2010), v. I, Osnovy teorii, Izdatelskii tsentr SGPI, Slavyansk-na-Kubani, 2010 , 196 pp.
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