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Abanin, Alexander Vasilievich
Professor
Doctor of physico-mathematical sciences (1996)
Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date: 6.02.1955
E-mail: ,
Website: https://sfedu.ru/person/avabanin
Keywords: theory of duality; ultradifferentiable functions and ultradistributions; Fourier transformation; representing systems; entire functions; extension of infinitely differentiable functions by Whitney.

Subject:

Some new criteria for weakly sufficient sets in weighted spaces of holomorphic functions were obtained. A connection between weakly sufficient sets and effective sets in the sense of G. Iyer was completely investigated. Geometric type criteria for representation of holomorphic functions by series of generalized exponentials were obtained. A complete description of generating ideals in rings of entire functions was found in terms of their generators (with I. S. Shabarshina). A criterion that spaces of ultradifferentiable functions of Beurling or of Roumier type admit an analog of Whitney's extension theorem was obtained.

Biography

Graduated from Faculty of Mechanics and Mathematics of Rostov State University (RSU) in 1977 (department of the theory of functions and functional analysis). Ph.D. thesis was defended in 1981. D.Sci. thesis was defended in 1995. A list of my works contains more than 100 titles. Since 1995 I and Yu. F. Korobeinik have led the research seminar at RSU on linear problems in analysis.
   
Main publications:
  • Abanin A. V. On Whitney's extension theorem for spaces of ultradifferentiable functions // Math. Ann., 2001, 320, 115–126.
  • Abanin A. V., Shabarshina I. S. Zero sets of generators and differential ideals // Math. Nachr., 2002, 238, 5–15.

https://www.mathnet.ru/eng/person17892
List of publications on Google Scholar
https://mathscinet.ams.org/mathscinet/MRAuthorID/229628
https://elibrary.ru/author_items.asp?authorid=4698
https://orcid.org/0000-0003-4507-4508
https://www.scopus.com/authid/detail.url?authorId=6505788204
https://www.researchgate.net/profile/Alexander-Abanin

Publications in Math-Net.Ru Citations
2023
1. A. V. Abanin, R. S. Mannanikov, “Weighted composition operators on quasi-Banach weighted sequence spaces”, Vladikavkaz. Mat. Zh., 25:4 (2023),  5–19  mathnet
2020
2. A. V. Abanin, V. A. Bogachev, G. G. Braichev, A. O. Vatulyan, M. I. Karyakin, Yu. A. Kiryutenko, A. G. Kusraev, Le Hai Khoi, I. M. Mal'tsev, S. N. Melikhov, Yu. S. Nalbandjan, Yu. A. Ustinov, Ha Huy Bang, V. B. Sherstyukov, “Yuri Fedorovich Korobeinik (on his 90's anniversary)”, Vladikavkaz. Mat. Zh., 22:3 (2020),  151–157  mathnet
3. A. V. Abanin, Yu. V. Korablina, “Boundedness of classical operators in weighted spaces of holomorphic functions”, Vladikavkaz. Mat. Zh., 22:3 (2020),  5–17  mathnet
2018
4. A. V. Abanin, T. M. Andreeva, “Analytic Description of the Spaces Dual to Spaces of Holomorphic Functions of Given Growth on Carathéodory Domains”, Mat. Zametki, 104:3 (2018),  323–335  mathnet  mathscinet  elib 1
5. A. V. Abanin, T. M. Andreeva, “On the surjectivity of the convolution operator in spaces of holomorphic functions of a prescribed growth”, Vladikavkaz. Mat. Zh., 20:2 (2018),  3–15  mathnet  elib
2017
6. A. V. Abanin, Ph. T. Tien, “Classical operators in weighted Banach spaces of holomorphic functions”, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 142 (2017),  3–13  mathnet  mathscinet  zmath; Journal of Mathematical Sciences, 241:6 (2019), 647–657 1
7. A. V. Abanin, T. I. Abanina, “On composition operators on Hilbert spaces of entire functions”, Izv. Vyssh. Uchebn. Zaved. Mat., 2017, no. 10,  3–7  mathnet; Russian Math. (Iz. VUZ), 61:10 (2017), 1–4  isi  scopus 4
2015
8. A. V. Abanin, Le Hai Khoi, “Linear continuous right inverse operator for convolution operator in spaces of holomorphic functions of polynomial growth”, Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 1,  3–13  mathnet; Russian Math. (Iz. VUZ), 59:1 (2015), 1–10  scopus 1
9. A. V. Abanin, “Sampling sets for the space of holomorphic functions of polynomial growth in a ball”, Ufimsk. Mat. Zh., 7:4 (2015),  3–14  mathnet  elib; Ufa Math. J., 7:4 (2015), 3–14 3
2013
10. A. V. Abanin, V. A. Varziev, “Sufficient sets in weighted Fréchet spaces of entire functions”, Sibirsk. Mat. Zh., 54:4 (2013),  725–741  mathnet  mathscinet; Siberian Math. J., 54:4 (2013), 575–587  isi  scopus 5
11. A. V. Abanin, P. S. Sergunin, Pham Trong Tien, “Weighted Fréchet spaces of entire functions from the class of power series spaces of finite type”, Vladikavkaz. Mat. Zh., 15:3 (2013),  3–6  mathnet
2012
12. A. V. Abanin, V. A. Varziev, “Representing systems of exponential functions in spaces of holomorphic functions with given growth near boundary”, Vladikavkaz. Mat. Zh., 14:4 (2012),  5–9  mathnet
13. A. V. Abanin, S. V. Petrov, “Minimal absolutely representing systems of exponential functions in spaces of analytic functions with given boundary smoothness”, Vladikavkaz. Mat. Zh., 14:3 (2012),  13–30  mathnet 2
2010
14. A. V. Abanin, D. A. Abanina, “Division theorem in some weighted spaces of entire functions”, Vladikavkaz. Mat. Zh., 12:3 (2010),  3–20  mathnet  elib 8
2008
15. A. V. Abanin, “$\Omega$-ultradistributions”, Izv. RAN. Ser. Mat., 72:2 (2008),  3–38  mathnet  mathscinet  zmath  elib; Izv. Math., 72:2 (2008), 207–240  isi  elib  scopus 6
16. A. V. Abanin, “On the multipliers of the space of entire functions defined by a nonradial binomial weight”, Vladikavkaz. Mat. Zh., 10:4 (2008),  10–16  mathnet  mathscinet  elib 2
17. A. V. Abanin, Pham Chong Tien, “Stability zones for slowly changing weights used in the theory of ultra-differentiable functions”, Vladikavkaz. Mat. Zh., 10:2 (2008),  3–8  mathnet  mathscinet  elib
2006
18. A. V. Abanin, I. A. Filip'ev, “Analytic implementation of the duals of some spaces of infinitely differentiable functions”, Sibirsk. Mat. Zh., 47:3 (2006),  485–500  mathnet  mathscinet  zmath  elib; Siberian Math. J., 47:3 (2006), 397–409  isi  elib  scopus 21
2005
19. A. V. Abanin, “On the isomorphism of spaces of ultradifferentiable functions of Beurling type”, Izv. Vyssh. Uchebn. Zaved. Mat., 2005, no. 4,  3–7  mathnet  mathscinet  zmath  elib; Russian Math. (Iz. VUZ), 49:4 (2005), 1–5 2
20. A. V. Abanin, “On Brannan's problem for sufficient sets”, Vladikavkaz. Mat. Zh., 7:3 (2005),  5–10  mathnet  mathscinet  elib
21. A. V. Abanin, “On an application of weakly sufficient sets”, Vladikavkaz. Mat. Zh., 7:2 (2005),  11–16  mathnet  mathscinet  elib 1
2004
22. A. V. Abanin, Yu. S. Nalbandyan, I. S. Shabarshina, “Continuation of infinitely differentiable functions to entire functions with consistent estimates for growth, and theorems of Paley-Wiener-Schwartz type”, Vladikavkaz. Mat. Zh., 6:2 (2004),  3–9  mathnet  mathscinet  zmath 1
2003
23. A. V. Abanin, I. S. Shabarshina, “Characterization of Generating Ideals in Some Rings of Entire Functions”, Mat. Zametki, 74:4 (2003),  483–493  mathnet  mathscinet  zmath; Math. Notes, 74:4 (2003), 459–468  isi  scopus 5
2000
24. A. V. Abanin, G. A. Semenova, “A generalization of the Laurent series”, Mat. Zametki, 68:1 (2000),  3–12  mathnet  mathscinet  zmath; Math. Notes, 68:1 (2000), 3–11  isi
1995
25. A. V. Abanin, “Generators in general classes of weighted spaces of holomorphic functions”, Dokl. Akad. Nauk, 342:4 (1995),  439–441  mathnet  mathscinet  zmath
26. A. V. Abanin, “Modification of L. Hörmander's method in the problem of generators and its applications”, Izv. Vyssh. Uchebn. Zaved. Mat., 1995, no. 8,  3–12  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 39:8 (1995), 1–10 1
27. A. V. Abanin, “Nontrivial expansions of zero and absolutely representing systems”, Mat. Zametki, 57:4 (1995),  483–497  mathnet  mathscinet  zmath; Math. Notes, 57:4 (1995), 335–344  isi 14
1993
28. A. V. Abanin, Yu. S. Nalbandjan, “Absolutely representing systems of exponentials of minimal type in spaces of functions with prescribed growth near the boundary”, Izv. Vyssh. Uchebn. Zaved. Mat., 1993, no. 10,  73–76  mathnet  mathscinet  zmath; Russian Math. (Iz. VUZ), 37:10 (1993), 72–75 3
1992
29. A. V. Abanin, “Geometric criteria for representing analytic functions by series of generalized exponentials”, Dokl. Akad. Nauk, 323:5 (1992),  807–810  mathnet  mathscinet  zmath; Dokl. Math., 45:2 (1992), 407–411 4
1991
30. A. V. Abanin, “Characterization of minimal systems of exponents of representative systems of generalized exponentials”, Izv. Vyssh. Uchebn. Zaved. Mat., 1991, no. 2,  3–12  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 35:2 (1991), 1–12 5
31. A. V. Abanin, “Distribution of indices of representing systems of generated exponents”, Mat. Zametki, 49:2 (1991),  3–13  mathnet  mathscinet  zmath; Math. Notes, 49:2 (1991), 117–124  isi 4
1987
32. A. V. Abanin, “On the continuation and stability of weakly sufficient sets”, Izv. Vyssh. Uchebn. Zaved. Mat., 1987, no. 4,  3–10  mathnet  mathscinet  zmath; Soviet Math. (Iz. VUZ), 31:4 (1987), 1–10 5
1986
33. A. V. Abanin, “Certain criteria for weak sufficiency”, Mat. Zametki, 40:4 (1986),  442–454  mathnet  mathscinet  zmath; Math. Notes, 40:4 (1986), 757–764  isi 13
1983
34. A. V. Abanin, “Distribution of effective sets and interior-extendability of Mittag-Leffler representing systems”, Mat. Zametki, 33:5 (1983),  657–668  mathnet  mathscinet  zmath; Math. Notes, 33:5 (1983), 339–344  isi 1
1979
35. A. V. Abanin, “Problem concerning a system of elements being a basis in its linear span”, Funktsional. Anal. i Prilozhen., 13:4 (1979),  53  mathnet  mathscinet  zmath; Funct. Anal. Appl., 13:4 (1979), 278–279
2021
36. A. V. Abanin, O. G. Avsyankin, V. I. Burenkov, B. G. Vakulov, S. K. Vodopyanov, M. L. Gol'dman, V. S. Guliev, I. M. Erusalimskyi, A. N. Karapetyants, M. I. Karyakin, V. M. Kokilashvili, A. G. Kusraev, E. R. Liflyand, A. V. Pskhu, V. S. Rabinovich, S. V. Rogozin, B. S. Rubin, A. P. Soldatov, I. M. Spitkovsky, V. D. Stepanov, Kh. G. Umarov, S. M. Umarkhadzhiev, “Stefan Grigorievich Samko (on the occasion of his 80th birthday)”, Vladikavkaz. Mat. Zh., 23:3 (2021),  126–129  mathnet
2020
37. A. V. Abanin, A. O. Vatulyan, M. I. Karyakin, S. B. Klimentov, Yu. F. Korobeinik, A. G. Kusraev, V. A. Stukopin, “Sergej Nikolaevich Melikhov (on his 60's anniversary)”, Vladikavkaz. Mat. Zh., 22:2 (2020),  98–99  mathnet
2018
38. A. V. Abanin, E. K. Basaeva, A. O. Vatulyan, S. K. Vodop'yanov, A. E. Gutman, V. A. Koibaev, Yu. F. Korobeinik, S. B. Klimentov, S. S. Kutateladze, A. A. Makhnev, B. B. Tasoev, S. M. Umarkhadzhiev, M. Z. Hudalov, “To the 65-th anniversary of prof. A. G. Kusraev”, Vladikavkaz. Mat. Zh., 20:2 (2018),  111–119  mathnet
2017
39. A. V. Abanin, S. N. Askhabov, A. B. Borisov, R. A. Bostanov, A. V. Zhiber, V. E. Zakharov, S. B. Klimentov, Yu. F. Korobeinik, A. G. Kusraev, S. S. Kutateladze, A. V. Mikhailov, A. P. Soldatov, Kh. G. Umarov, S. M. Umarkhadzhiev, “Alexey Borisovich Shabat (on his 80's anniversary)”, Vladikavkaz. Mat. Zh., 19:3 (2017),  83–85  mathnet
2013
40. A. V. Abanin, A. V. Belokon', M. I. Karyakin, Yu. F. Korobeinik, A. G. Kusraev, A. V. Nasedkin, Yu. A. Ustinov, O. V. Yavruyan, “Vatul'yan Aleksandr Ovanesovich (on his 60th birthday)”, Vladikavkaz. Mat. Zh., 15:4 (2013),  91–94  mathnet
2012
41. A. V. Abanin, V. P. Zakharyuta, M. I. Karyakin, Yu. F. Korobeinik, A. G. Kusraev, “Dragilev Mikhail Mikhailovich (on his 90th birthday)”, Vladikavkaz. Mat. Zh., 14:4 (2012),  95–98  mathnet
42. A. V. Abanin, S. N. Askhabov, A. B. Borisov, R. A. Bostanov, A. V. Zhiber, V. E. Zakharov, S. B. Klimentov, Yu. F. Korobeinik, A. G. Kusraev, S. S. Kutateladze, A. V. Mikhailov, A. P. Soldatov, Kh. G. Umarov, S. M. Umarkhadzhiev, “Shabat Aleksei Borisovich (on his 75th birthday)”, Vladikavkaz. Mat. Zh., 14:2 (2012),  71–73  mathnet
2011
43. A. V. Abanin, Yu. A. Kiryutenko, Yu. F. Korobeinik, A. G. Kusraev, S. N. Melikhov, “Valentin Vasil'evich Napalkov (on his seventieth birthday)”, Vladikavkaz. Mat. Zh., 13:3 (2011),  70–71  mathnet
2004
44. A. V. Abanin, M. M. Dragilev, A. I. Efimov, S. B. Klimentov, Yu. F. Korobeĭnik, A. G. Kusraev, V. F. Pulyaev, V. G. Fetisov, “Vladimir Petrovich Kondakov (on the occasion of his sixtieth birthday)”, Vladikavkaz. Mat. Zh., 6:2 (2004),  58–60  mathnet  mathscinet  zmath
1994
45. A. V. Abanin, “Letter to the editor”, Mat. Zametki, 56:5 (1994),  140  mathnet  mathscinet  zmath; Math. Notes, 56:5 (1994), 1193–1194

Presentations in Math-Net.Ru
1. Topological properties of classical operators in weighted spaces of holomorphic functions
A. V. Abanin
International Conference "Theory of Functions, Operator Theory and Quantum Information Theory"
June 2, 2023 16:30
2. Динамические свойства оператора дифференцирования в весовых пространствах целых функций
A. V. Abanin

March 28, 2023 17:30
3. Mikhail Mikhailovich Dragilev: Outstanding mathematician and teacher
A. V. Abanin
Modern methods, problems and applications of operator theory and harmonic analysis
August 24, 2022 14:30   

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