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Abanin Alexander Vasilievich

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Total publications: 36
Scientific articles: 29

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This page:2408
Abstract pages:5956
Full texts:1940
References:596
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: ,
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.

http://www.mathnet.ru/eng/person17892
List of publications on Google Scholar
List of publications on ZentralBlatt
https://mathscinet.ams.org/mathscinet/MRAuthorID/229628

Publications in Math-Net.Ru
1. Analytic Description of the Spaces Dual to Spaces of Holomorphic Functions of Given Growth on Carathéodory Domains
A. V. Abanin, T. M. Andreeva
Mat. Zametki, 104:3 (2018),  323–335
2. Classical operators in weighted Banach spaces of holomorphic functions
A. V. Abanin, Ph. T. Tien
Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 142 (2017),  3–13
3. On composition operators on Hilbert spaces of entire functions
A. V. Abanin, T. I. Abanina
Izv. Vyssh. Uchebn. Zaved. Mat., 2017, no. 10,  3–7
4. Linear continuous right inverse operator for convolution operator in spaces of holomorphic functions of polynomial growth
A. V. Abanin, Le Hai Khoi
Izv. Vyssh. Uchebn. Zaved. Mat., 2015, no. 1,  3–13
5. Sampling sets for the space of holomorphic functions of polynomial growth in a ball
A. V. Abanin
Ufimsk. Mat. Zh., 7:4 (2015),  3–14
6. Sufficient sets in weighted Fréchet spaces of entire functions
A. V. Abanin, V. A. Varziev
Sibirsk. Mat. Zh., 54:4 (2013),  725–741
7. Weighted Fréchet spaces of entire functions from the class of power series spaces of finite type
A. V. Abanin, P. S. Sergunin, Pham Trong Tien
Vladikavkaz. Mat. Zh., 15:3 (2013),  3–6
8. Representing systems of exponential functions in spaces of holomorphic functions with given growth near boundary
A. V. Abanin, V. A. Varziev
Vladikavkaz. Mat. Zh., 14:4 (2012),  5–9
9. Minimal absolutely representing systems of exponential functions in spaces of analytic functions with given boundary smoothness
A. V. Abanin, S. V. Petrov
Vladikavkaz. Mat. Zh., 14:3 (2012),  13–30
10. Division theorem in some weighted spaces of entire functions
A. V. Abanin, D. A. Abanina
Vladikavkaz. Mat. Zh., 12:3 (2010),  3–20
11. $\Omega$-ultradistributions
A. V. Abanin
Izv. RAN. Ser. Mat., 72:2 (2008),  3–38
12. On the multipliers of the space of entire functions defined by a nonradial binomial weight
A. V. Abanin
Vladikavkaz. Mat. Zh., 10:4 (2008),  10–16
13. Stability zones for slowly changing weights used in the theory of ultra-differentiable functions
A. V. Abanin, Pham Chong Tien
Vladikavkaz. Mat. Zh., 10:2 (2008),  3–8
14. Analytic implementation of the duals of some spaces of infinitely differentiable functions
A. V. Abanin, I. A. Filip'ev
Sibirsk. Mat. Zh., 47:3 (2006),  485–500
15. On the isomorphism of spaces of ultradifferentiable functions of Beurling type
A. V. Abanin
Izv. Vyssh. Uchebn. Zaved. Mat., 2005, no. 4,  3–7
16. On Brannan's problem for sufficient sets
A. V. Abanin
Vladikavkaz. Mat. Zh., 7:3 (2005),  5–10
17. On an application of weakly sufficient sets
A. V. Abanin
Vladikavkaz. Mat. Zh., 7:2 (2005),  11–16
18. Continuation of infinitely differentiable functions to entire functions with consistent estimates for growth, and theorems of Paley-Wiener-Schwartz type
A. V. Abanin, Yu. S. Nalbandyan, I. S. Shabarshina
Vladikavkaz. Mat. Zh., 6:2 (2004),  3–9
19. Characterization of Generating Ideals in Some Rings of Entire Functions
A. V. Abanin, I. S. Shabarshina
Mat. Zametki, 74:4 (2003),  483–493
20. A generalization of the Laurent series
A. V. Abanin, G. A. Semenova
Mat. Zametki, 68:1 (2000),  3–12
21. Modification of L. Hörmander's method in the problem of generators and its applications
A. V. Abanin
Izv. Vyssh. Uchebn. Zaved. Mat., 1995, no. 8,  3–12
22. Nontrivial expansions of zero and absolutely representing systems
A. V. Abanin
Mat. Zametki, 57:4 (1995),  483–497
23. Absolutely representing systems of exponentials of minimal type in spaces of functions with prescribed growth near the boundary
A. V. Abanin, Yu. S. Nalbandjan
Izv. Vyssh. Uchebn. Zaved. Mat., 1993, no. 10,  73–76
24. Characterization of minimal systems of exponents of representative systems of generalized exponentials
A. V. Abanin
Izv. Vyssh. Uchebn. Zaved. Mat., 1991, no. 2,  3–12
25. Distribution of indices of representing systems of generated exponents
A. V. Abanin
Mat. Zametki, 49:2 (1991),  3–13
26. On the continuation and stability of weakly sufficient sets
A. V. Abanin
Izv. Vyssh. Uchebn. Zaved. Mat., 1987, no. 4,  3–10
27. Certain criteria for weak sufficiency
A. V. Abanin
Mat. Zametki, 40:4 (1986),  442–454
28. Distribution of effective sets and interior-extendability of Mittag-Leffler representing systems
A. V. Abanin
Mat. Zametki, 33:5 (1983),  657–668
29. Problem concerning a system of elements being a basis in its linear span
A. V. Abanin
Funktsional. Anal. i Prilozhen., 13:4 (1979),  53

30. Alexey Borisovich Shabat (on his 80's anniversary)
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
Vladikavkaz. Mat. Zh., 19:3 (2017),  83–85
31. Vatul'yan Aleksandr Ovanesovich (on his 60th birthday)
A. V. Abanin, A. V. Belokon', M. I. Karyakin, Yu. F. Korobeinik, A. G. Kusraev, A. V. Nasedkin, Yu. A. Ustinov, O. V. Yavruyan
Vladikavkaz. Mat. Zh., 15:4 (2013),  91–94
32. Dragilev Mikhail Mikhailovich (on his 90th birthday)
A. V. Abanin, V. P. Zakharyuta, M. I. Karyakin, Yu. F. Korobeinik, A. G. Kusraev
Vladikavkaz. Mat. Zh., 14:4 (2012),  95–98
33. Shabat Aleksei Borisovich (on his 75th birthday)
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
Vladikavkaz. Mat. Zh., 14:2 (2012),  71–73
34. Valentin Vasil'evich Napalkov (on his seventieth birthday)
A. V. Abanin, Yu. A. Kiryutenko, Yu. F. Korobeinik, A. G. Kusraev, S. N. Melikhov
Vladikavkaz. Mat. Zh., 13:3 (2011),  70–71
35. Vladimir Petrovich Kondakov (on the occasion of his sixtieth birthday)
A. V. Abanin, M. M. Dragilev, A. I. Efimov, S. B. Klimentov, Yu. F. Korobeĭnik, A. G. Kusraev, V. F. Pulyaev, V. G. Fetisov
Vladikavkaz. Mat. Zh., 6:2 (2004),  58–60
36. Letter to the editor
A. V. Abanin
Mat. Zametki, 56:5 (1994),  140

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