Baskakov, Anatoly Grigorievich

Total publications: 82 (81)
in MathSciNet: 76 (75)
in zbMATH: 70 (69)
in Web of Science: 48 (47)
in Scopus: 54 (54)
Cited articles: 70
Citations in Math-Net.Ru: 1130
Citations in Web of Science: 32
Citations in Scopus: 667

Number of views:
This page:18146
Abstract pages:42627
Full texts:9947
Doctor of physico-mathematical sciences (1988)
Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date: 21.07.1944
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.


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.


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.
List of publications on Google Scholar

Full list of scientific publications:
| scientific publications | by years | by types | by times cited in WoS | by times cited in Scopus | common list |

1. 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  mathnet  crossref

2. 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  mathnet  crossref  mathscinet  isi  scopus (cited: 3);
3. A. G. Baskakov, D. B. Didenko, “Spectral Analysis of Operator Polynomials and Second-Order Differential Operators”, Math. Notes, 108:4 (2020), 477–491  mathnet  crossref  crossref  mathscinet  isi  elib  scopus
4. 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  mathnet  crossref
5. 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  mathnet  crossref
6. 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  mathnet  crossref  mathscinet  isi  scopus;

7. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus (cited: 1)
8. A. G. Baskakov, E. E. Dikarev, “Spectral theory of functions in studying partial differential operators”, Ufa Math. J., 11:1 (2019), 3–18  mathnet  crossref  mathscinet  isi  scopus (cited: 2)
9. 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  mathnet  crossref

10. A. G. Baskakov, V. B. Didenko, “On invertibility states of differential and difference operators”, Izv. Math., 82:1 (2018), 1–13  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus (cited: 5)
11. 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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus (cited: 4)
12. 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  mathnet  crossref  mathscinet  isi  scopus (cited: 10)
13. 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  mathnet  crossref  mathscinet  zmath  isi  elib  scopus

14. 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  mathnet  crossref  mathscinet  zmath  isi  scopus (cited: 2)
15. A. G. Baskakov, V. D. Kharitonov, “Spectral Analysis of Operator Polynomials and Higher-Order Difference Operators”, Math. Notes, 101:3 (2017), 391–405  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  scopus (cited: 3)
16. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 25)  elib  elib  scopus (cited: 25)

17. A. Baskakov, I. Strukova, “Harmonic analysis of functions periodic at infinity”, Eurasian Math. J., 7:4 (2016), 9–29  mathnet (cited: 11)  mathscinet  isi
18. A. G. Baskakov, D. M. Polyakov, “Spectral Properties of the Hill Operator”, Math. Notes, 99:4 (2016), 598–602  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 7)  elib  elib  scopus (cited: 6)

19. A. G. Baskakov, A. Yu. Duplishcheva, “Difference operators and operator-valued matrices of the second order”, Izv. Math., 79:2 (2015), 217–232  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus (cited: 4)
20. 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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus (cited: 21)
21. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus (cited: 11)

22. 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  mathnet  crossref  mathscinet  zmath  scopus (cited: 4)

23. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus (cited: 24)

24. 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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus (cited: 12)

25. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus (cited: 38)
26. A. G. Baskakov, A. A. Vorobjev, M. Yu. Romanova, “Hyperbolic Operator Semigroups and Lyapunov's Equation”, Math. Notes, 89:2 (2011), 194–205  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus (cited: 3)

27. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus (cited: 21)
28. A. G. Baskakov, K. A. Sintyaeva, “On the Bohr–Favard inequalities for operators”, Russian Math. (Iz. VUZ), 53:12 (2009), 11–17  mathnet  crossref  mathscinet  zmath  elib

29. A. G. Baskakov, “Linear Relations as Generators of Semigroups of Operators”, Math. Notes, 84:2 (2008), 166–183  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus (cited: 7)

30. A. G. Baskakov, “Fredholm differential and difference operators”, Dokl. Math., 76:2 (2007), 669–672  mathnet  crossref  mathscinet  zmath  elib  elib  scopus (cited: 3)
31. A. G. Baskakov, A. S. Zagorskii, “Spectral Theory of Linear Relations on Real Banach Spaces”, Math. Notes, 81:1 (2007), 15–27  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus (cited: 9)

32. A. G. Baskakov, I. A. Krishtal, “On Harmonic Analysis of Causal Operators”, Funct. Anal. Appl., 40:1 (2006), 52–55  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus (cited: 3)
33. 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  mathnet
34. 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  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
35. 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  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib

36. A. G. Baskakov, I. A. Krishtal, “Harmonic analysis of causal operators and their spectral properties”, Izv. Math., 69:3 (2005), 439–486  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus (cited: 19)

37. 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  mathnet  crossref  mathscinet  zmath  elib  scopus (cited: 25)

38. A. G. Baskakov, “Estimates of Bounded Solutions of Linear Differential Equations”, Differ. Equ., 39:3 (2003), 447–450  mathnet  crossref  mathscinet  zmath  scopus (cited: 4)

39. A. G. Baskakov, K. I. Chernyshov, “Linear Relations, Differential Inclusions, and Degenerate Semigroups”, Funct. Anal. Appl., 36:4 (2002), 306–310  mathnet  crossref  crossref  mathscinet  zmath  isi  scopus (cited: 3)
40. A. G. Baskakov, “Splitting of perturbated differential operators with unbounded operator coefficients”, Fundam. Prikl. Mat., 8:1 (2002), 1–16  mathnet  mathscinet  zmath
41. A. G. Baskakov, K. I. Chernyshov, “Spectral analysis of linear relations and degenerate operator semigroups”, Sb. Math., 193:11 (2002), 1573–1610  mathnet  crossref  crossref  mathscinet  zmath  isi  scopus (cited: 42)

42. A. G. Baskakov, “Spectral Analysis of Linear Differential Operators and Semigroups of Finite-Difference Operators: II”, Differ. Equ., 37:1 (2001), 1–10  mathnet  crossref  mathscinet  zmath  scopus (cited: 2)
43. A. G. Baskakov, “On the invertibility of linear difference operators with constant coefficients”, Russian Math. (Iz. VUZ), 45:5 (2001), 1–9  mathnet  mathscinet  zmath  adsnasa
44. 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  mathnet  crossref  mathscinet  zmath  isi  scopus (cited: 22)

45. A. G. Baskakov, “Invertibility and the Fredholm property of difference operators”, Math. Notes, 67:6 (2000), 690–698  mathnet  crossref  crossref  mathscinet  zmath  isi  scopus (cited: 16)

46. 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  mathnet  crossref  crossref  mathscinet  zmath  isi  scopus (cited: 2)
47. A. G. Baskakov, “On correct linear differential operators”, Sb. Math., 190:3 (1999), 323–348  mathnet  crossref  crossref  mathscinet  zmath  isi  scopus (cited: 17)

48. A. G. Baskakov, “Spectral analysis of linear differential operators, and semigroups of difference operators. I”, Differ. Equ., 33:10 (1997), 1305–1312  mathnet  mathscinet  zmath
49. A. G. Baskakov, “Estimates for the entries of inverse matrices and the spectral analysis of linear operators”, Izv. Math., 61:6 (1997), 1113–1135  mathnet  crossref  crossref  mathscinet  zmath  isi  scopus (cited: 18)
50. A. G. Baskakov, “Spectral analysis of difference operators with strongly continuous coefficients”, Russian Math. (Iz. VUZ), 41:10 (1997), 1–10  mathnet  mathscinet  zmath
51. A. G. Baskakov, “Asymptotic estimates for elements of matrices of inverse operators, and harmonic analysis”, Siberian Math. J., 38:1 (1997), 10–22  mathnet  crossref  mathscinet  zmath  isi  scopus (cited: 25)
52. A. G. Baskakov, “Spectral analysis of difference operators”, Dokl. Akad. Nauk, 353:5 (1997), 587–589  mathnet  mathscinet  zmath

53. A. G. Baskakov, “Semigroups of Difference Operators in Spectral Analysis of Linear Differential Operators”, Funct. Anal. Appl., 30:3 (1996), 149–157  mathnet  crossref  crossref  mathscinet  zmath  isi  scopus (cited: 52)
54. A. G. Baskakov, “Linear differential operators with unbounded operator coefficients and semigroups of bounded operators”, Math. Notes, 59:6 (1996), 586–593  mathnet  crossref  crossref  mathscinet  zmath  isi  scopus (cited: 15)

55. A. G. Baskakov, “Spectral analysis of linear differential operators and semigroups of difference operators”, Dokl. Math., 52:1 (1995), 30–32  mathnet  mathscinet  zmath
56. A. G. Baskakov, “On Spectral Properties of Some Classes of Linear Operators”, Funct. Anal. Appl., 29:2 (1995), 121–123  mathnet  crossref  mathscinet  zmath  isi  scopus (cited: 1)
57. A. G. Baskakov, “Spectral analysis of perturbed nonquasianalytic and spectral operators”, Russian Acad. Sci. Izv. Math., 45:1 (1995), 1–31  mathnet  crossref  mathscinet  zmath  adsnasa  adsnasa  isi  scopus (cited: 16)

58. 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  mathnet  mathscinet  zmath
59. A. G. Baskakov, “The Beurling spectrum in the analysis of certain classes of Banach algebras”, Russian Math. Surveys, 49:4 (1994), 151–152  mathnet  crossref  mathscinet  zmath  adsnasa  isi  scopus (cited: 1)
60. A. G. Baskakov, “Some conditions for the invertibility of linear differential and difference operators”, Dokl. Math., 48:3 (1994), 498–501  mathnet  mathscinet  zmath

61. A. G. Baskakov, “Abstract harmonic analysis and asymptotic estimates of elements of inverse matrices”, Math. Notes, 52:2 (1992), 764–771  mathnet  crossref  mathscinet  zmath  isi  scopus (cited: 10)
62. A. G. Baskakov, Chan Khyu Bong, “On the almost periodicity of solutions of linear functional equations”, Dokl. Math., 45:3 (1992), 509–512  mathnet  mathscinet  zmath
63. A. G. Baskakov, “On the splitting of a differential operator with unbounded operator coefficients”, Dokl. Math., 45:2 (1992), 329–333  mathnet  mathscinet  zmath

64. A. G. Baskakov, Chan Khyu Bong, “Spectral properties of bounded solutions of linear functional-differential equations”, Dokl. Math., 46:1 (1993), 74–78  mathnet  mathscinet  zmath

65. 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  mathnet  mathscinet  zmath
66. A. G. Baskakov, “Spectral analysis with respect to finite-dimensional perturbations of spectral operators”, Soviet Math. (Iz. VUZ), 35:1 (1991), 1–11  mathnet  mathscinet  zmath  adsnasa
67. A. G. Baskakov, “Dichotomy of the spectrum of non-self-adjoint operators”, Siberian Math. J., 32:3 (1991), 370–375  mathnet  crossref  mathscinet  zmath  isi  scopus (cited: 5)

68. A. G. Baskakov, “Wiener's theorem and the asymptotic estimates of the elements of inverse matrices”, Funct. Anal. Appl., 24:3 (1990), 222–224  mathnet  crossref  mathscinet  zmath  isi  scopus (cited: 61)

69. A. G. Baskakov, T. K. Katsaran, “Spectral analysis of integro-differential operators with nonlocal boundary conditions”, Differ. Equ., 24:8 (1988), 934–941  mathnet  mathscinet  zmath
70. A. G. Baskakov, “Operator ergodic theorems and complementability of subspaces of Banach spaces”, Soviet Math. (Iz. VUZ), 32:11 (1988), 1–14  mathnet  mathscinet  zmath

71. A. G. Baskakov, Garmonicheskii analiz lineinykh operatorov, Izdatelstvo VGU, Voronezh, 1987 , 164 pp.
72. 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  mathnet  crossref  mathscinet  zmath  scopus (cited: 18)

73. A. G. Baskakov, “The averaging method in the theory of perturbations of linear differential operators”, Differ. Uravn., 21:4 (1985), 555–562  mathnet  mathscinet  zmath
74. A. G. Baskakov, “Regularized trace formulas for powers of perturbed spectral operators”, Soviet Math. (Iz. VUZ), 29:8 (1985), 93–96  mathnet  mathscinet  zmath

75. A. G. Baskakov, “The method of similar operators and formulas for regularized traces”, Soviet Math. (Iz. VUZ), 28:3 (1984), 1–13  mathnet  mathscinet  zmath

76. A. G. Baskakov, “Harmonic analysis of cosine and exponential operator-valued functions”, Math. USSR-Sb., 52:1 (1985), 63–90  mathnet  crossref  mathscinet  zmath  scopus (cited: 8)

77. A. G. Baskakov, “Spectral synthesis in Banach modules over commutative Banach algebras”, Math. Notes, 34:4 (1983), 776–782  mathnet  crossref  mathscinet  zmath  isi  scopus (cited: 8)
78. A. G. Baskakov, “Methods of abstract harmonic analysis in the theory of perturbations of linear operators”, Siberian Math. J., 24:1 (1983), 17–32  mathnet  crossref  mathscinet  zmath  isi  scopus (cited: 24)

79. A. G. Baskakov, “On Ditkin's condition in some Beurling algebras”, Izv. Vyssh. Uchebn. Zaved. Mat., 1982, no. 1, 3–5  mathnet  mathscinet  zmath

80. A. G. Baskakov, “General ergodic theorems in Banach modules”, Funct. Anal. Appl., 14:3 (1980), 215–217  mathnet  crossref  mathscinet  zmath  isi  scopus (cited: 7)

81. A. G. Baskakov, “Bernstein-type inequalities in abstract harmonic analysis”, Siberian Math. J., 20:5 (1979), 665–672  mathnet  crossref  mathscinet  zmath  isi  scopus (cited: 8)

82. A. G. Baskakov, “Spectral criteria for almost periodicity of solutions of functional equations”, Math. Notes, 24:2 (1978), 606–612  mathnet  crossref  mathscinet  zmath  scopus (cited: 17)

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