01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
21.07.1944
E-mail:
Keywords:
spectral theory of linear operators,
Banach algebras,
abstract harmonic analysis,
Banach modules,
differential equations in Banach spaces,
linear relations,
Linear differential operators,
spectrum of operators,
functional homogeneous spaces,
Green Function,
Fredholm operator,
Dirac operator,
spectrum asymptotic,
spectral distribution,
similar operators method.
Subject:
The spectral criteria for almost periodicity of abstract equations in Banach spaces were obtained. A new class of commutative Banach algebras with radical was introduced and studied. The spectral theory of Banach modules over such algebras was constructed. The method of similar operators for perturbed linear operators with discrete spectrum is developed. Estimates of the elements of the inverse matrix were obtained and applied to the spectral theory of linear operators. The spectral properties of abstract parabolic operators were studied by means of the methods of the theory operator semigroups. Basic elements of the spectral theory of linear relations (linear multivalued operators) were established and applied in the study of the degenerate differential equations.
Biography
Graduated from the department of Mathematics and Mechanics of Voronezh State University in 1969. Ph.D. — 1973, D.Sc. — 1987. The list of papers contains more than 100 titles. Since 1983 I have led a research seminar on operator theory at Voronezh State University.
Soros professor.
Main publications:
Baskakov A. G. Spektralnye kriterii pochti periodichnosti reshenii funktsionalnykh uravnenii // Matematicheskie zametki, 1978. T. 24, # 2. S. 195–206.
Baskakov A. G. Spektralnyi analiz vozmuschennykh nekvazianaliticheskikh i spektralnykh operatorov // Izvestiya RAN, seriya matematicheskaya, 1994. T. 58, # 4. S. 3–32.
Baskakov A. G. Polugruppy raznostnykh operatorov v spektralnom analize lineinykh differentsialnykh operatorov // Funktsionalnyi analiz i ego prilozheniya, 1996. T. 30, # 3. S. 1–11.
Baskakov A. G. Otsenki elementov obratnykh matrits i spektralnyi analiz lineinykh operatorov // Izvestiya RAN, seriya matematicheskaya, 1997. T. 61, # 6. S. 3–26.
Baskakov A. G., Chernyshov K. I. Spektralnyi analiz lineinykh otnoshenii i vyrozhdennye polugruppy operatorov // Matematicheskii sbornik, 2002. T. 193, # 11. S. 3–35.
A. G. Baskakov, G. V. Garkavenko, N. B. Uskova, L. N. Kostina, “On equivalent operators”, Proceedings of the Voronezh international spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXV”, Voronezh, April 26-30, 2024, Part 1, Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 235, VINITI, Moscow, 2024, 3–14
2023
2.
A. G. Baskakov, G. V. Garkavenko, N. B. Uskova, “Application of the method of similar operators to some classes of difference operators”, Differential Equations and Mathematical Physics, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 225, VINITI, Moscow, 2023, 14–27
3.
A. G. Baskakov, G. V. Garkavenko, N. B. Uskova, “On the algebra of integral operators with involution”, Proceedings of the Voronezh international spring mathematical school “Modern methods of the theory of boundary-value problems. Pontryagin readings—XXXIV”, Voronezh, May 3-9, 2023, Part 1, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 230, VINITI, Moscow, 2023, 41–49
4.
A. G. Baskakov, G. V. Garkavenko, N. B. Uskova, “On bounded difference operators with involution”, Proceedings of the Voronezh international winter mathematical school “Modern methods of function theory and related problems”, Voronezh, January 27 - February 1, 2023, Part 3, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 229, VINITI, Moscow, 2023, 12–21
2022
5.
A. G. Baskakov, G. V. Garkavenko, I. A. Krishtal, N. B. Uskova, “Method of similar operators in the problem of bi-invariant subspaces”, Proceedings of the Voronezh spring mathematical school
“Modern methods of the theory of boundary-value problems. Pontryagin readings – XXXI”.
Voronezh, May 3-9, 2020, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 204, VINITI, Moscow, 2022, 3–15
6.
A. G. Baskakov, I. A. Krishtal, N. B. Uskova, “On smoothing the operator coefficient of a first-order differential operator in a Banach space”, Proceedings of the Voronezh International Winter Mathematical School “Modern Methods of Function Theory and Related Problems”, Voronezh, January 28 - February 2, 2021, Part 1, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 206, VINITI, Moscow, 2022, 3–14
2021
7.
A. G. Baskakov, G. V. Garkavenko, N. B. Uskova, “On matrices with summable diagonals”, 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 5, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 194, VINITI, Moscow, 2021, 23–37
8.
A. G. Baskakov, G. V. Garkavenko, I. A. Krishtal, N. B. Uskova, “The method of similar operators in the spectral analysis of infinite operator matrices. Examples II”, Applied Mathematics & Physics, 53:3 (2021), 205–212
2020
9.
A. G. Baskakov, I. A. Krishtal, N. B. Uskova, “On the spectral analysis of a differential operator with an involution and general boundary conditions”, Eurasian Math. J., 11:2 (2020), 30–39;
A. G. Baskakov, D. B. Didenko, “Spectral Analysis of Operator Polynomials and Second-Order Differential Operators”, Math. Notes, 108:4 (2020), 477–491
11.
A. G. Baskakov, I. A. Krishtal, N. B. Uskova, “The method of similar operators in the spectral analysis of infinite operator matrices. Examples I.”, Applied Mathematics & Physics, 52:3 (2020), 185–194
12.
A. G. Baskakov, I. A. Krishtal, N. B. Uskova, “The method of similar operators in the spectral analysis of infinite operator matrices”, Applied Mathematics & Physics, 52:2 (2020), 71–85
13.
A. G. Baskakov, V. E. Strukov, I. I. Strukova, “Almost periodic at infinity functions from homogeneous spaces as solutions to differential equations with unbounded operator coefficients”, Eurasian Math. J., 11:4 (2020), 8–24;
2019
14.
A. G. Baskakov, V. E. Strukov, I. I. Strukova, “Harmonic analysis of functions in homogeneous spaces and harmonic distributions that are periodic or almost periodic at infinity”, Sb. Math., 210:10 (2019), 1380–1427
15.
A. G. Baskakov, E. E. Dikarev, “Spectral theory of functions in studying partial differential operators”, Ufa Math. J., 11:1 (2019), 3–18
16.
A. G. Baskakov, I. A. Krishtal, N. B. Uskova, “Method of Similar Operators in the Study of Spectral Properties of Perturbed First-Order Differential Operators”, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 171, 2019, 3–18
2018
17.
A. G. Baskakov, V. B. Didenko, “On invertibility states of differential and difference operators”, Izv. Math., 82:1 (2018), 1–13
18.
A. G. Baskakov, I. I. Strukova, I. A. Trishina, “Solutions almost periodic at infinity to differential equations with unbounded operator coefficients”, Siberian Math. J., 59:2 (2018), 231–242
19.
A. G. Baskakov, N. B. Uskova, “Fourier method for first order differential equations with involution and groups of operators”, Ufa Math. J., 10:3 (2018), 11–34
20.
A. G. Baskakov, V. E. Strukov, I. I. Strukova, “On the almost periodic at infinity functions from homogeneous spaces”, Probl. anal. Issues Anal., 7(25):2 (2018), 3–19
2017
21.
A. G. Baskakov, T. K. Katsaran, T. I. Smagina, “Linear differential second-order equations in Banach space and splitting of operators”, Russian Math. (Iz. VUZ), 61:10 (2017), 32–43
22.
A. G. Baskakov, V. D. Kharitonov, “Spectral Analysis of Operator Polynomials and Higher-Order Difference Operators”, Math. Notes, 101:3 (2017), 391–405
23.
A. G. Baskakov, D. M. Polyakov, “The method of similar operators in the spectral analysis of the Hill operator with nonsmooth potential”, Sb. Math., 208:1 (2017), 1–43
2016
24.
A. Baskakov, I. Strukova, “Harmonic analysis of functions periodic at infinity”, Eurasian Math. J., 7:4 (2016), 9–29
A. G. Baskakov, D. M. Polyakov, “Spectral Properties of the Hill Operator”, Math. Notes, 99:4 (2016), 598–602
2015
26.
A. G. Baskakov, A. Yu. Duplishcheva, “Difference operators and operator-valued matrices of the second order”, Izv. Math., 79:2 (2015), 217–232
27.
A. G. Baskakov, “Harmonic and Spectral Analysis of Power Bounded Operators and Bounded Semigroups of Operators on Banach Spaces”, Math. Notes, 97:2 (2015), 164–178
28.
A. G. Baskakov, “Estimates for the Green's function and parameters of exponential dichotomy of a hyperbolic operator semigroup and linear relations”, Sb. Math., 206:8 (2015), 1049–1086
2014
29.
A. G. Baskakov, N. S. Kaluzhina, D. M. Polyakov, “Slowly varying on infinity semigroups of operators”, Russian Math. (Iz. VUZ), 58:7 (2014), 1–10
2013
30.
A. G. Baskakov, “Analysis of linear differential equations by methods of the spectral theory of difference operators and linear relations”, Russian Math. Surveys, 68:1 (2013), 69–116
2012
31.
A. G. Baskakov, N. S. Kaluzhina, “Beurlings theorem for functions with essential spectrum from homogeneous spaces and stabilization of solutions of parabolic equations”, Math. Notes, 92:5 (2012), 587–605
2011
32.
A. G. Baskakov, A. V. Derbushev, A. O. Shcherbakov, “The method of similar operators in the spectral analysis of non-self-adjoint Dirac operators with non-smooth potentials”, Izv. Math., 75:3 (2011), 445–469
33.
A. G. Baskakov, A. A. Vorobjev, M. Yu. Romanova, “Hyperbolic Operator Semigroups and Lyapunov's Equation”, Math. Notes, 89:2 (2011), 194–205
2009
34.
A. G. Baskakov, “Spectral analysis of differential operators with unbounded operator-valued coefficients, difference relations and semigroups of difference relations”, Izv. Math., 73:2 (2009), 215–278
35.
A. G. Baskakov, K. A. Sintyaeva, “On the Bohr–Favard inequalities for operators”, Russian Math. (Iz. VUZ), 53:12 (2009), 11–17
2008
36.
A. G. Baskakov, “Linear Relations as Generators of Semigroups of Operators”, Math. Notes, 84:2 (2008), 166–183
2007
37.
A. G. Baskakov, “Fredholm differential and difference operators”, Dokl. Math., 76:2 (2007), 669–672
38.
A. G. Baskakov, A. S. Zagorskii, “Spectral Theory of Linear Relations on Real Banach Spaces”, Math. Notes, 81:1 (2007), 15–27
2006
39.
A. G. Baskakov, I. A. Krishtal, “On Harmonic Analysis of Causal Operators”, Funct. Anal. Appl., 40:1 (2006), 52–55
40.
A. G. Baskakov, V. V. Obukhovskii, P. Zecca, “On differential inclusions in uniform spaces of functions”, Izv. IMI UdGU, 2006, no. 3(37), 7–8
41.
A. G. Baskakov, K. I. Chernyshov, “On Distribution Semigroups with a Singularity at Zero and Bounded Solutions of Differential Inclusions”, Math. Notes, 79:1 (2006), 18–30
42.
R. A. Arhontova, A. G. Baskakov, I. A. Bakhtin, E. S. Belyaeva, Yu. G. Borisovich, A. S. Grechenko, V. R. Zachepa, A. A. Karatsuba, A. F. Kudinov, V. V. Obukhovskii, A. I. Perov, A. S. Potapov, E. M. Semenov, V. P. Trofimov, N. N. Udodenko, “Kirill Andreevich Rodosskii (obituary)”, Russian Math. Surveys, 61:5 (2006), 971–973
2005
43.
A. G. Baskakov, I. A. Krishtal, “Harmonic analysis of causal operators and their spectral properties”, Izv. Math., 69:3 (2005), 439–486
2006
44.
A. G. Baskakov, “Representation theory for Banach algebras, Abelian groups, and semigroups in the spectral analysis of linear operators”, Journal of Mathematical Sciences, 137:4 (2006), 4885–5036
2003
45.
A. G. Baskakov, “Estimates of Bounded Solutions of Linear Differential Equations”, Differ. Equ., 39:3 (2003), 447–450
2002
46.
A. G. Baskakov, K. I. Chernyshov, “Linear Relations, Differential Inclusions, and Degenerate Semigroups”, Funct. Anal. Appl., 36:4 (2002), 306–310
47.
A. G. Baskakov, “Splitting of perturbated differential operators with unbounded operator coefficients”, Fundam. Prikl. Mat., 8:1 (2002), 1–16
48.
A. G. Baskakov, K. I. Chernyshov, “Spectral analysis of linear relations and degenerate operator semigroups”, Sb. Math., 193:11 (2002), 1573–1610
2001
49.
A. G. Baskakov, “Spectral Analysis of Linear Differential Operators and Semigroups of Finite-Difference Operators: II”, Differ. Equ., 37:1 (2001), 1–10
50.
A. G. Baskakov, “On the invertibility of linear difference operators with constant coefficients”, Russian Math. (Iz. VUZ), 45:5 (2001), 1–9
51.
A. G. Baskakov, A. I. Pastukhov, “Spectral analysis of a weighted shift operator with unbounded operator coefficients”, Siberian Math. J., 42:6 (2001), 1026–1036
2000
52.
A. G. Baskakov, “Invertibility and the Fredholm property of difference operators”, Math. Notes, 67:6 (2000), 690–698
1999
53.
A. G. Baskakov, “An Abstract Analog of the Krylov–Bogolyubov Transformation in the Perturbation Theory of Linear Operators”, Funct. Anal. Appl., 33:2 (1999), 144–147
54.
A. G. Baskakov, “On correct linear differential operators”, Sb. Math., 190:3 (1999), 323–348
1997
55.
A. G. Baskakov, “Spectral analysis of linear differential operators, and semigroups of difference operators. I”, Differ. Equ., 33:10 (1997), 1305–1312
56.
A. G. Baskakov, “Estimates for the entries of inverse matrices and the spectral analysis of linear operators”, Izv. Math., 61:6 (1997), 1113–1135
57.
A. G. Baskakov, “Spectral analysis of difference operators with strongly continuous coefficients”, Russian Math. (Iz. VUZ), 41:10 (1997), 1–10
58.
A. G. Baskakov, “Asymptotic estimates for elements of matrices of inverse operators, and harmonic analysis”, Siberian Math. J., 38:1 (1997), 10–22
59.
A. G. Baskakov, “Spectral analysis of difference operators”, Dokl. Akad. Nauk, 353:5 (1997), 587–589
1996
60.
A. G. Baskakov, “Semigroups of Difference Operators in Spectral Analysis of Linear Differential Operators”, Funct. Anal. Appl., 30:3 (1996), 149–157
61.
A. G. Baskakov, “Linear differential operators with unbounded operator coefficients and semigroups of bounded operators”, Math. Notes, 59:6 (1996), 586–593
1995
62.
A. G. Baskakov, “Spectral analysis of linear differential operators and semigroups of difference operators”, Dokl. Math., 52:1 (1995), 30–32
63.
A. G. Baskakov, “On Spectral Properties of Some Classes of Linear Operators”, Funct. Anal. Appl., 29:2 (1995), 121–123
64.
A. G. Baskakov, “Spectral analysis of perturbed nonquasianalytic and spectral operators”, Russian Acad. Sci. Izv. Math., 45:1 (1995), 1–31
1994
65.
A. G. Baskakov, V. V. Yurgelas, “Circular dichotomy of the spectrum of a class of nonselfadjoint operators”, Russian Math. (Iz. VUZ), 38:10 (1994), 10–15
66.
A. G. Baskakov, “The Beurling spectrum in the analysis of certain classes of Banach algebras”, Russian Math. Surveys, 49:4 (1994), 151–152
67.
A. G. Baskakov, “Some conditions for the invertibility of linear differential and difference operators”, Dokl. Math., 48:3 (1994), 498–501
1992
68.
A. G. Baskakov, “Abstract harmonic analysis and asymptotic estimates of elements of inverse matrices”, Math. Notes, 52:2 (1992), 764–771
69.
A. G. Baskakov, Chan Khyu Bong, “On the almost periodicity of solutions of linear functional equations”, Dokl. Math., 45:3 (1992), 509–512
70.
A. G. Baskakov, “On the splitting of a differential operator with unbounded operator coefficients”, Dokl. Math., 45:2 (1992), 329–333
1993
71.
A. G. Baskakov, Chan Khyu Bong, “Spectral properties of bounded solutions of linear functional-differential equations”, Dokl. Math., 46:1 (1993), 74–78
1991
72.
A. G. Baskakov, “Spectral properties of the differential operator $\frac d{dt}-A_0$ with an unbounded operator $A_0$”, Differ. Uravn., 27:12 (1991), 2162–2164
73.
A. G. Baskakov, “Spectral analysis with respect to finite-dimensional perturbations of spectral operators”, Soviet Math. (Iz. VUZ), 35:1 (1991), 1–11
74.
A. G. Baskakov, “Dichotomy of the spectrum of non-self-adjoint operators”, Siberian Math. J., 32:3 (1991), 370–375
1990
75.
A. G. Baskakov, “Wiener's theorem and the asymptotic estimates of the elements of inverse matrices”, Funct. Anal. Appl., 24:3 (1990), 222–224
1988
76.
A. G. Baskakov, T. K. Katsaran, “Spectral analysis of integro-differential operators with nonlocal boundary conditions”, Differ. Equ., 24:8 (1988), 934–941
77.
A. G. Baskakov, “Operator ergodic theorems and complementability of subspaces of Banach spaces”, Soviet Math. (Iz. VUZ), 32:11 (1988), 1–14
1987
78.
A. G. Baskakov, Garmonicheskii analiz lineinykh operatorov, Izdatelstvo VGU, Voronezh, 1987 , 164 pp.
79.
A. G. Baskakov, “A theorem on splitting an operator, and some related questions in the analytic theory of perturbations”, Math. USSR-Izv., 28:3 (1987), 421–444
1985
80.
A. G. Baskakov, “The averaging method in the theory of perturbations of linear differential operators”, Differ. Uravn., 21:4 (1985), 555–562
81.
A. G. Baskakov, “Regularized trace formulas for powers of perturbed spectral operators”, Soviet Math. (Iz. VUZ), 29:8 (1985), 93–96
1984
82.
A. G. Baskakov, “The method of similar operators and formulas for regularized traces”, Soviet Math. (Iz. VUZ), 28:3 (1984), 1–13
1985
83.
A. G. Baskakov, “Harmonic analysis of cosine and exponential operator-valued functions”, Math. USSR-Sb., 52:1 (1985), 63–90
1983
84.
A. G. Baskakov, “Spectral synthesis in Banach modules over commutative Banach algebras”, Math. Notes, 34:4 (1983), 776–782
85.
A. G. Baskakov, “Methods of abstract harmonic analysis in the theory of perturbations of linear operators”, Siberian Math. J., 24:1 (1983), 17–32
1982
86.
A. G. Baskakov, “On Ditkin's condition in some Beurling algebras”, Izv. Vyssh. Uchebn. Zaved. Mat., 1982, no. 1, 3–5
1980
87.
A. G. Baskakov, “General ergodic theorems in Banach modules”, Funct. Anal. Appl., 14:3 (1980), 215–217
1979
88.
A. G. Baskakov, “Bernstein-type inequalities in abstract harmonic analysis”, Siberian Math. J., 20:5 (1979), 665–672
1978
89.
A. G. Baskakov, “Spectral criteria for almost periodicity of solutions of functional equations”, Math. Notes, 24:2 (1978), 606–612
2024
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