Gubreev, Gennady Mychaylovich

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Total publications: 29
Scientific articles: 29

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Doctor of physico-mathematical sciences (1995)
Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date: 18.05.1948
Keywords: non-selfadjoint operators; characteristic operator-function; spectral theory of conractions; finite dementional perturbation of Volterra operators; matrix Muckenhoupt weights; Hilbert space of entire functions; functional models of operators; unconditional bases; oneparametric semiqroups of operators.


It was obtained the description of unconditional bases from values of kernels,which are generated by Muchenhoupt weights on the special contours. It was investigated the shift operators in new Hilbert spaces of entire functions. The problem of free interpalation with entire function of finite order from special classes have been formulated and solved. It was suggested the method of integral estimates the norms of resolvents of finite dimentional perturbations of Volterra operators for investigation the special structure such operators. It was found an application the analytic functions from unit disk from Jerbashian classes to spectral theory of non-weak contractions. It was given a description of generators of $C_0$-semigroups, inverse to which are finite dimentianal perturbation of Volterra operators.


Graduated from Faculty of Mathematics and Mechanics of Kharkov state university in 1971 (department of mathematical physics). Ph.D. thesis was defendent in 1978. D.Sci. thesis was defended in 1995. A list of my work contains near 50 titles.

Main publications:
  • Gubreev G. M. Jerbachian A. M. Functions of generalized bounded type in spectral theory of non-weak contractions // Journal of Operator Theory, 1991, 26, 155–190.
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List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. G. M. Gubreev, V. N. Levchuk, “Description of Unconditional Bases Formed by Values of the Dunkl Kernels”, Funktsional. Anal. i Prilozhen., 49:1 (2015),  79–82  mathnet  zmath  elib; Funct. Anal. Appl., 49:1 (2015), 64–66  isi  scopus
2. G. M. Gubreev, A. A. Tarasenko, “On the Similarity to Self-Adjoint Operators”, Funktsional. Anal. i Prilozhen., 48:4 (2014),  65–70  mathnet  mathscinet  zmath  elib; Funct. Anal. Appl., 48:4 (2014), 286–290  isi  scopus
3. G. M. Gubreev, G. D. Urum, “On a Class of Convolution Operators on a Finite Interval”, Mat. Zametki, 96:5 (2014),  653–657  mathnet  mathscinet  zmath  elib; Math. Notes, 96:5 (2014), 647–650  isi  scopus
4. G. M. Gubreev, A. A. Tarasenko, “A Criterion for the Unconditional Basis Property of Eigenvectors for Finite-Rank Perturbations of Volterra Operators”, Funktsional. Anal. i Prilozhen., 45:2 (2011),  86–91  mathnet  mathscinet  zmath; Funct. Anal. Appl., 45:2 (2011), 149–153  isi  scopus
5. G. M. Gubreev, Yu. D. Latushkin, “Functional models of non-selfadjoint operators, strongly continuous semigroups, and matrix Muckenhoupt weights”, Izv. RAN. Ser. Mat., 75:2 (2011),  69–126  mathnet  mathscinet  zmath  elib; Izv. Math., 75:2 (2011), 287–346  isi  scopus
6. G. M. Gubreev, A. A. Tarasenko, “Spectral decomposition of model operators in de Branges spaces”, Mat. Sb., 201:11 (2010),  41–76  mathnet  mathscinet  zmath  elib; Sb. Math., 201:11 (2010), 1599–1634  isi  scopus
7. G. M. Gubreev, G. V. Lukashenko, “On a Class of Completely Continuous Operators in Hilbert Spaces”, Funktsional. Anal. i Prilozhen., 43:2 (2009),  75–79  mathnet  mathscinet  zmath; Funct. Anal. Appl., 43:2 (2009), 143–146  isi  scopus
8. G. M. Gubreev, Yu. D. Latushkin, “Perturbations of Strongly Continuous Operator Semigroups, and Matrix Muckenhoupt Weights”, Funktsional. Anal. i Prilozhen., 42:3 (2008),  85–89  mathnet  mathscinet  zmath  elib; Funct. Anal. Appl., 42:3 (2008), 234–238  isi  scopus
9. G. M. Gubreev, A. A. Tarasenko, “Unconditional Reproducing Kernel Bases in de Branges Spaces”, Funktsional. Anal. i Prilozhen., 40:1 (2006),  71–75  mathnet  mathscinet  zmath  elib; Funct. Anal. Appl., 40:1 (2006), 58–61  isi  scopus
10. G. M. Gubreev, “Regular Mittag-Leffler kernels and spectral decomposition of a class of non-selfadjoint operators”, Izv. RAN. Ser. Mat., 69:1 (2005),  17–60  mathnet  mathscinet  zmath  elib; Izv. Math., 69:1 (2005), 15–57  isi  scopus
11. G. M. Gubreev, “Regular Mittag-Leffler Kernels and Volterra Operators”, Funktsional. Anal. i Prilozhen., 38:4 (2004),  82–86  mathnet  mathscinet  zmath; Funct. Anal. Appl., 38:4 (2004), 305–308  isi  scopus
12. G. M. Gubreev, A. A. Tarasenko, “Representability of de Branges Matrices as Blaschke–Potapov Products and Completeness of Some Families of Functions”, Mat. Zametki, 73:6 (2003),  841–847  mathnet  mathscinet  zmath; Math. Notes, 73:6 (2003), 796–801  isi  scopus
13. G. M. Gubreev, M. G. Volkova, “Hilbert space unconditional bases formed by values of an entire vector-function of order 1/2”, Zap. Nauchn. Sem. POMI, 290 (2002),  33–41  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 124:2 (2004), 4861–4866
14. G. M. Gubreev, “The Structure of Model Volterra Operators, Biorthogonal Expansions, and Interpolation in Regular de Branges Spaces”, Funktsional. Anal. i Prilozhen., 35:2 (2001),  74–78  mathnet  mathscinet  zmath  elib; Funct. Anal. Appl., 35:2 (2001), 142–145  isi  scopus
15. G. M. Gubreev, “Spectral theory of regular quasi-exponentials and regular $B$-representable vector functions (the projection method: 20 years later)”, Algebra i Analiz, 12:6 (2000),  1–97  mathnet  mathscinet  zmath; St. Petersburg Math. J., 12:6 (2001), 875–947
16. G. M. Gubreev, “Unconditional Bases of Hilbert Spaces Composed of Values of Entire Vector Functions of Exponential Type”, Funktsional. Anal. i Prilozhen., 33:1 (1999),  62–65  mathnet  mathscinet  zmath; Funct. Anal. Appl., 33:1 (1999), 52–55  isi
17. G. M. Gubreev, “$L_2$-stable semigroups, Muckenhoupt weights, and unconditional bases of values of quasi-exponentials”, Mat. Sb., 190:12 (1999),  3–36  mathnet  mathscinet  zmath; Sb. Math., 190:12 (1999), 1715–1747  isi  scopus
18. G. M. Gubreev, E. I. Olefir, “Unconditional bases, the matrix Muckenhoupt condition, and Carleson series in the spectrum”, Zap. Nauchn. Sem. POMI, 262 (1999),  90–126  mathnet  mathscinet  zmath; J. Math. Sci. (New York), 110:5 (2002), 2955–2978
19. G. M. Gubreev, V. N. Pyvovarchyk, “Spectral Analysis of the Regge Problem with Parameters”, Funktsional. Anal. i Prilozhen., 31:1 (1997),  70–74  mathnet  mathscinet  zmath; Funct. Anal. Appl., 31:1 (1997), 54–57  isi
20. G. M. Gubreev, “On one class of bases in Hilbert spaces and the similarity problem for volterra operators”, Funktsional. Anal. i Prilozhen., 26:4 (1992),  64–67  mathnet  mathscinet  zmath; Funct. Anal. Appl., 26:4 (1992), 282–284  isi
21. G. M. Gubreev, “On a class of unconditional bases in Hilbert spaces and on the problem of similarity of dissipative Volterra operators”, Mat. Sb., 183:9 (1992),  105–146  mathnet  mathscinet  zmath; Russian Acad. Sci. Sb. Math., 77:1 (1994), 93–126  isi
22. G. M. Gubreev, “Spectral analysis of biorthogonal expansions generated by Muckenhoupt weights”, Zap. Nauchn. Sem. LOMI, 190 (1991),  34–80  mathnet  mathscinet  zmath; J. Math. Sci., 71:1 (1994), 2192–2221
23. G. M. Gubreev, “Spectral analysis of biorthogonal expansions of functions, and exponential series”, Izv. Akad. Nauk SSSR Ser. Mat., 53:6 (1989),  1236–1268  mathnet  mathscinet  zmath; Math. USSR-Izv., 35:3 (1990), 573–605
24. G. M. Gubreev, “Basis property of families of Mittag-Leffler-type functions, the dzhrbashyan transformations, and the muckenhoupt condition”, Funktsional. Anal. i Prilozhen., 21:4 (1987),  71–72  mathnet  mathscinet  zmath; Funct. Anal. Appl., 21:4 (1987), 317–319  isi
25. G. M. Gubreev, “Mean-periodic extensions of functions”, Funktsional. Anal. i Prilozhen., 20:1 (1986),  67–68  mathnet  mathscinet  zmath; Funct. Anal. Appl., 20:1 (1986), 56–58  isi
26. G. M. Gubreev, “Spectral analysis of the differentiation operator and the Muckenhoupt condition”, Dokl. Akad. Nauk SSSR, 278:5 (1984),  1052–1056  mathnet  mathscinet  zmath
27. G. M. Gubreev, “A theorem on uniform correctness of a Cauchy problem and its application”, Funktsional. Anal. i Prilozhen., 18:2 (1984),  89–91  mathnet  mathscinet  zmath; Funct. Anal. Appl., 18:2 (1984), 163–165  isi
28. G. M. Gubreev, A. I. Kovalenko, “Tests for completeness of root subspaces of a differentiation operator with abstract boundary conditions”, Mat. Zametki, 30:4 (1981),  543–552  mathnet  mathscinet  zmath; Math. Notes, 30:4 (1981), 765–770  isi
29. G. M. Gubreev, A. I. Kovalenko, “On a criterion for the equality $D_A=D_{A^*}$ for dissipative operators”, Dokl. Akad. Nauk SSSR, 254:5 (1980),  1044–1047  mathnet  mathscinet  zmath

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