Scientific interests: entire functions, asymptotics of functions, represented by exponential serie. Polyas problem (set by him in 1929) for Dirichlet serie with Fejer gaps.
Biography
Graduated from Bashikirian state unversity in 1978 (department of theory of functions and functional analysis). D.Sci. thesis was defended in 1996. A list of my works contains more than 40 titles.
Main publications:
A.M. Gaisin, “Usilennaya nepolnota sistemy eksponent i problema Makintaira”, Matematicheskii sbornik, 182:7 (1991), 931–945
T. I. Belous, A. M. Gaisin, R. A. Gaisin, “An estimate for the sum of a Dirichlet series on an arc of bounded slope”, Izv. Vyssh. Uchebn. Zaved. Mat., 2024, no. 1, 3–13
2.
T. I. Belous, A. M. Gaisin, R. A. Gaisin, “Specification of asymptotic Pólya type estimate for Dirichlet series converging in half–plane”, Ufa Math. J., 16:4 (2024), 12–20
2023
3.
A. M. Gaisin, R. A. Gaisin, “Levinson-type theorem and Dyn'kin problems”, Sb. Math., 214:5 (2023), 676–702
4.
A. M. Gaisin, G. A. Gaisina, “On the stability of the maximum term of the Dirichlet series”, Russian Math. (Iz. VUZ), 67:1 (2023), 20–29
5.
A. M. Gaisin, G. A. Gaisina, “Refinement of Macintyre — Evgrafov type theorems”, Chelyab. Fiz.-Mat. Zh., 8:3 (2023), 309–318
6.
N. N. Aitkuzhina, A. M. Gaisin, R. A. Gaisin, “Regular growth of Dirichlet series of the class $D(\Phi)$ on curves of bounded $K$-slope”, Probl. anal. Issues Anal., 12(30):3 (2023), 3–19;
N. N. Aitkuzhina, A. M. Gaisin, R. A. Gaisin, “Behavior of entire Dirichlet series of class $\underline{D}(\Phi)$ on curves of bounded $K$-slope”, Ufa Math. J., 15:3 (2023), 3–12
8.
A. M. Gaisin, R. A. Gaisin, T. I. Belous, “Regularity of the growth of Dirichlet series with respect to a strongly incomplete exponential system”, Sibirsk. Mat. Zh., 64:4 (2023), 742–752
2022
9.
A. M. Gaisin, B. E. Kanguzhin, A. A. Seitova, “Completeness of the exponential system on a segment of the real axis”, Eurasian Math. J., 13:2 (2022), 37–42
A. M. Gaisin, T. I. Belous, “Maximal term of Dirichlet series converging in half-plane: stability theorem”, Ufa Mathematical Journal, 14:3 (2022), 22–32
11.
A. M. Gaisin, N. N. Autkukhina, “Stability criterion for maximal terms of Dirichlet series”, Journal of Math. Sci., 260:6 (2022), 715–724
12.
A. M. Gaisin, G. A. Gaisina, “Representation of analytic functions by exponential series in half-plane”, Lob. Journal of Math., 43:6 (2022), 1513–1518
13.
A. M. Gaisin, N. N. Aitkuzhina, “Stability-preserving perturbation of the maximal terms of Dirichlet series”, Probl. Anal. Issues Anal., 11:3 (2022), 1–15
A. M. Gaisin, G. A. Gaisina, “Behavior of Coefficients of Series of Exponentials of Finite Order Near the Boundary”, Journal of Mathematical Sciences, 257:3 (2021), 286–295
2020
15.
A. M. Gaisin, G. A. Gaisina, “Teoremy tipa Ritta - Sugimury”, Vladikavkazskii matematicheskii zhurnal, 22:3 (2020), 47–57
A. M. Gaisin, G. A. Gaisina, “Behavior of coefficients of series of exponents of finite order near the boundary”, Complex Analysis. Mathematical Physics, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 162, VINITI, Moscow, 2019, 15–24
2018
17.
A. M. Gaisin, “Extremal problems in nonquasianalytic Carleman classes. Applications”, Sb. Math., 209:7 (2018), 958–984
18.
A. M. Gaisin, N. N. Aitkuzhina, “Poryadok ryada Dirikhle s neregulyarnym raspredeleniem pokazatelei v polupolosakh”, Algebra i analiz, 30:4 (2018), 27–46; A. M. Gaisin, N. N. Aitkuzhina, “The order of a Dirichlet series with an irregular distribution of the exponents in the half-strip”, St. Petersburg Math. J., 30:4 (2019), 639–653
A. M. Gaisin, G. A. Gaisina, “Order of Dirichlet series with regular distribution of exponents in half-strips”, Ufa Math. J., 10:4 (2018), 50–63
2019
20.
A. M. Gaisin, N. N. Aitkuzhina, “The order of the Dirichlet series in the half-strip”, Journal of Mathematical Sciences, 241:6 (2019), 686–700
2017
21.
A. M. Gaisin, G. A. Gaisina, “Estimate for growth and decay of functions in Macintyre–Evgrafov kind theorems”, Ufa Math. Journal, 9:3 (2017), 26–36
22.
A. M. Gaisin, Aleksei Fedorovich Leontev (1917 – 1987): osnovnye napravleniya issledovanii i vklad v nauku, RITs BashGU, Ufa, 2017 , 40 pp.
23.
A. M. Gaisin, “Osnovopolozhnik ufimskoi matematicheskoi shkoly (k stoletiyu so dnya rozhdeniya A.F. Leonteva)”, Vestnik AN RB, 22:1 (2017), 94–101
24.
A. M. Gaisin, Tselye funktsii: osnovy klassicheskoi teorii s prilozheniyami k issledovaniyam po kompleksnomu analizu, 2-e izd., RITs BashGU, Ufa, 2017 , 160 pp.
25.
A. M. Gaisin, “Alexey Fedorovich Leont'ev (to his centenary)”, Ufa Math. Journal, 9:3 (2017), 3–7
26.
A. F. Leontev, Predstavlenie funktsii ryadami eksponent, eds. A. M. Gaisin, Dialog, Ufa, 2017 , 128 pp.
2016
27.
A. M. Gaisin, Tselye funktsii: osnovy klassicheskoi teorii s prilozheniyami k issledovaniyam po kompleksnomu analizu, Monografiya, RITs BashGU, Ufa, 2016 , 160 pp.
28.
A. M. Gaisin, R. A. Gaisin, “Incomplete system of exponentials on arcs and nonquasianalytic Carleman classes. II”, St. Petersburg Math. J., 27:1 (2016), 33–50
2015
29.
N. N. Aitkuzhina, A. M. Gaisin, “Exactness of estimates for $k$th order of Dirichlet series in a semi-strip”, Ufa Math. Journal, 7:4 (2015), 15–23
30.
A. M. Gaisin, T. I. Belous, “Effektivnaya otsenka monotonnoi funktsii”, Matematicheskie metody i informatsionnye tekhnologii v sotsialno-ekonomicheskoi sfere, Sb. statei po mater. vserossiiskoi konferentsii, Nauchno-izd. tsentr «Aeterna», Ufa, 2015, 16–21
2014
31.
N. N. Aitkuzhina, A. M. Gaisin, “$k$-order estimate for Dirichlet series in a half-strip”, Ufa Math. Journal, 6:4 (2014), 18–30
2013
32.
A. M. Gaisin, “Minimum of modulus of the sum of Dirichlet series converging in a half-plane”, Ufa Math. Journal, 5:4 (2013), 49–57
33.
N. N. Aitkuzhina, A. M. Gaisin, “Dirichlet series with real coefficients”, Ufa Math. Journal, 5:3 (2013), 3–10
2012
34.
A. M. Gaisin, Zh. G. Rakhmatullina, “Iterations of entire transcendental functions with a regular behavior of the modulus minimum”, Ufimsk. Mat. Zh., 4:1 (2012), 38–46
35.
A. M. Gaisin, T. I. Belous, Ryady Fure, Uchebnoe elektronnoe izdanie, UGATU, Ufa, 2012 , 65 pp., Nomer gos. registr. – 0321204201
2011
36.
A. M. Gaisin, Zh. G. Rakhmatullina, “An estimate for the sum of a Dirichlet series in terms of the minimum of its modulus on a vertical line segment”, Sb. Math., 202:12 (2011), 1741–1773
2010
37.
A. M. Gaisin, Zh. G. Rakhmatullina, “Behavior of the modulus minimum of the Dirichlet series on the system of segments”, Ufimsk. Mat. Zh., 2:3 (2010), 39–45
38.
A. M. Gaisin, Zh. G. Rakhmatullina, “Real sequences with Fejér gaps”, Ufimsk. Mat. Zh., 2:2 (2010), 27–40
39.
A. M. Gaisin, Teoremy tipa Borelya-Nevanlinny. Primeneniya, Uchebnoe posobie (rukovodstvo k primeneniyu v issledovaniyakh po teorii funktsii), RITs BashGU, Ufa, 2010 , 82 pp.
2009
40.
A. M. Gaisin, “Classes of Dirichlet Series with Real Coefficients Defined by Convex Majorants of a Growth”, Ufimsk. Mat. Zh., 1:4 (2009), 58–66
41.
A. M. Gaisin, N. N. Yusupova, “Behaviour of the Sum of Dirichlet Series with a given majorant of a growth on curves”, Ufimsk. Mat. Zh., 1:2 (2009), 17–28
42.
A. M. Gaisin, I. G. Kinzyabulatov, “Usilenno nepolnye sistemy eksponent”, Poet, uchenyi, pedagog, Materialy Vseros. konf., posv. 100-letiyu so dnya rozhdeniya N. A. Frolova (Syktyvkar, 13–14 aprelya 2009 g.), SyktGU, Syktyvkar, 2009, 91–95
43.
A. M. Gaisin, N. N. Yusupova, “O teoremakh edinstvennosti dlya ryadov Dirikhle”, Poet, uchenyi, pedagog, Materialy Vseros. konf., posv. 100-letiyu so dnya rozhdeniya N. A. Frolova (Syktyvkar, 13–14 aprelya 2009 g.), SyktGU, Syktyvkar, 2009, 96–100
2008
44.
A. M. Gaisin, “Levinson's Condition in the Theory of Entire Functions: Equivalent Statements”, Math. Notes, 83:3 (2008), 317–326
45.
A. M. Gaisin, I. G. Kinzyabulatov, “A Levinson-Sjöberg type theorem. Applications”, Sb. Math., 199:7 (2008), 985–1007
46.
A. M. Gaisin, D. I. Sergeeva, “An estimate for the Dirichlet series in a half-strip in the case of the irregular distribution of exponents. II”, Siberian Math. J., 49:2 (2008), 222–238
47.
A. M. Gaisin, I. G. Kinzyabulatov, “Nepolnye sistemy eksponent na dugakh”, Tr. Instituta matematiki s VTs UNTs RAN, Vyp. 1, RITs BashGU, Ufa, 2008, 50–60
2007
48.
A. M. Gaisin, “Dirichlet series with real coefficients that are unbounded on the positive half-axis”, Sb. Math., 198:6 (2007), 793–815
49.
A. M. Gaisin, D. I. Sergeeva, “Entire functions with a given sequence of zeros and of regular behavior on the real axis. I”, Siberian Math. J., 48:5 (2007), 798–808
50.
A. M. Gaisin, I. G. Kinzyabulatov, “Teorema tipa Levinsona i kvazianaliticheskie klassy funktsii”, Vestnik UGATU, 9:3 (21) (2007), 14–19
2006
51.
A. M. Gaisin, “Properties of series of exponentials whose exponents satisfy to a condition of Levinson type”, Sb. Math., 197:6 (2006), 813–833
2005
52.
A. M. Gaisin, I. D. Latypov, “Asymptotic Behavior of the Sum of the Dirichlet Series of Prescribed Growth on Curves”, Math. Notes, 78:1 (2005), 33–46
53.
A. M. Gaǐsin, D. I. Sergeeva, “Entire functions of exponential type with regular behavior on the real axis”, Vladikavkaz. Mat. Zh., 7:3 (2005), 31–37
2004
54.
A. M. Gaisin, I. D. Latypov, “An estimate for the Dirichlet series with Fejér gaps on the real axis”, Siberian Math. J., 45:1 (2004), 53–68
2003
55.
A. M. Gaisin, “Estimates of the growth and decrease on curves of an entire function of infinite order”, Sb. Math., 194:8 (2003), 1167–1194
56.
A. M. Gaisin, T. I. Belous, “Estimation over curves of the functions given by Dirichlet series on a half-plane”, Siberian Math. J., 44:1 (2003), 22–36
57.
A. M. Gaisin, “Razlichnye interpretatsii usloviya tipa Levinsona”, Vestnik UGATU, 4:2 (2003), 79–83
2002
58.
A. M. Gaisin, I. D. Latypov, “Asymptotics of the logarithm of the maximal term of a modified Dirichlet series”, Russian Math. (Iz. VUZ), 46:9 (2002), 13–22
59.
A. M. Gaisin, “Solution of the Polya problem”, Sb. Math., 193:6 (2002), 825–845
60.
A. M. Gaisin, T. I. Belous, “$B$-stability of the maximal term of the Hadamard composition of two Dirichlet series”, Siberian Math. J., 43:6 (2002), 1027–1038
61.
A. M. Gaisin, T. I. Belous, “Asimptoticheskie svoistva ryadov Dirikhle s lakunami Feiera”, Vestnik UGATU, 3:1 (2002), 65–72
2001
62.
A. M. Gaisin, “Maximal Term of the Modified Dirichlet Series”, Math. Notes, 69:6 (2001), 756–769
2000
63.
A. M. Gaisin, “Otsenka ryada Dirikhle s lakunami Feiera na krivykh”, Doklady RAN, 370:6 (2000), 735–737
A. M. Gaisin, T. I. Belous, “Asimptotika maksimalnogo chlena izmenennogo ryada Dirikhle”, Kompleksnyi analiz, differentsialnye uravneniya i smezhnye voprosy. I. Kompleksnyi analiz., Tr. mezhdunarodnoi konferentsii, IMVTs UNTs RAN, Ufa, 2000, 14–20
65.
A. M. Gaisin, “V – ustoichivost maksimalnogo chlena izmenennogo ryada Dirikhle”, Aktualnye problemy matematicheskogo analiza, Sb. nauchn. trudov, Izd-vo GinGo, Rostov-na-Donu, 2000, 58–66
1999
66.
A. M. Gaisin, Ryady Dirikhle s lakunami Feiera, Preprint. ISBN 5-13-000024-2, Institut matematiki s VTs UNTs RAN, Ufa, 1999 , 36 pp.
1998
67.
A. M. Gaisin, “On a theorem of Hayman”, Siberian Math. J., 39:3 (1998), 431–445
68.
A. M. Gaisin, Approksimatsiya v normirovannykh prostranstvakh, Uchebnoe posobie, Izd-vo BashGU, Ufa, 1998 , 84 pp.
1997
69.
A. M. Gaisin, “Asymptotic estimate of the sum of a Dirichlet series on curves”, Math. Notes, 61:6 (1997), 681–686
70.
A. M. Gaisin, “On a theorem of Pólya on entire functions with real Taylor coefficients”, Siberian Math. J., 38:1 (1997), 37–46
1996
71.
A. M. Gaisin, “An estimate of a Dirichlet series with real coefficients on a ray”, Math. Notes, 60:6 (1996), 611–621
72.
A. M. Gaisin, “Dirichlet series with rarely alternating real coefficients”, Siberian Math. J., 37:2 (1996), 245–252
1995
73.
A. M. Gaisin, “Behavior of logarithm of modulus of the sum of Dirichlet series on curves”, The Journal of Analysis (Madras), 3 (1995), 205–211
74.
A. M. Gaisin, “Behavior of the logarithm of the modulus value of the sum of a Dirichlet series converging in a half-plane”, Russian Acad. Sci. Izv. Math., 45:1 (1995), 175–186
75.
A. M. Gaisin, “On a conjecture of Polya”, Russian Acad. Sci. Izv. Math., 44:2 (1995), 281–299
76.
A. M. Gaisin, “An estimate for a Dirichlet series whose exponents are zeros of an entire function with irregular behavior”, Russian Acad. Sci. Sb. Math., 81:1 (1995), 163–183
1994
77.
A. M. Gaisin, “O roste summy ryada Dirikhle na luche”, Lineinye operatory v kompleksnom analize, Sb. statei, izd-vo RGU, Rostov-na-Donu, 1994, 27–34
1991
78.
A. M. Gaisin, “Behavior of the sum of a Dirichlet series having a prescribed growth”, Math. Notes, 50:4 (1991), 1018–1024
79.
A. M. Gaisin, “A uniqueness theorem for Dirichlet series”, Math. Notes, 50:2 (1991), 807–812
1992
80.
A. M. Gaisin, “Strong incompleteness of a system of exponentials, and Macintyre's problem”, Math. USSR-Sb., 73:2 (1992), 305–318
1990
81.
A. M. Gaisin, “Behavior of the sum of a series of exponentials near the boundary of the domain of regularity”, Math. Notes, 48:3 (1990), 904–910
82.
A. M. Gaisin, “Asimptoticheskoe povedenie summy tselogo ryada Dirikhle na krivykh”, Issledovaniya po teorii priblizhenii, Tr. Instituta matematiki s VTs, BNTs AN SSSR, Ufa, 1990, 3–15
1987
83.
A. M. Gaisin, “Behavior of the sum of a Dirichlet series in halfstrips”, Math. Notes, 42:5 (1987), 863–868
1984
84.
A. M. Gaisin, “Rost funktsii, predstavlennoi ryadom Dirikhle, na luche”, Issledovaniya po teorii approksimatsii funktsii, Tr. OFM BFAN SSSR, BFAN SSSR, Ufa, 1984, 20–29
85.
A. M. Gaisin, Otsenka rosta funktsii, predstavlennoi ryadom Dirikhle, na luche, Ruk. dep. v VINITI № 1000-84, 9 fevralya 1984
1983
86.
A. M. Gaisin, “Razlozhenie funktsii, analiticheskikh v poluploskosti i imeyuschikh konechnyi R-tip, v ryady eksponent”, Voprosy approksimatsii funktsii veschestvennogo i kompleksnogo peremennykh, Tr. OFM BFAN SSSR, BFAN SSSR, Ufa, 1983, 30–42
87.
A. M. Gaisin, “A bound for the growth in a half-strip of a function represented by a Dirichlet series”, Math. USSR-Sb., 45:3 (1983), 411–422
1982
88.
A. M. Gaisin, Razlozhenie funktsii, analiticheskikh v poluploskosti i imeyuschikh konechnyi poryadok rosta vblizi granitsy, v ryady eksponent, Ruk. dep. v VINITI № 2448-82, 14 maya 1982
89.
A. M. Gaisin, “O tipe funktsii, predstavlennoi ryadom Dirikhle v polupolose”, Voprosy approksimatsii funktsii kompleksnogo peremennogo, Tr. OFM BFAN SSSR, BFAN SSSR, Ufa, 1982, 3–15
1980
90.
A. M. Gaisin, “O roste funktsii, predstavlennoi ryadom Dirikhle, vblizi pryamoi skhodimosti”, Issledovaniya po teorii approksimatsii funktsii, Tr. OFM BFAN SSSR, BFAN SSSR, Ufa, 1980, 5–13
2024
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