Baskakov, Anatoly Grigorievich

Total publications: 68 (67)
in MathSciNet: 57 (56)
in zbMATH: 48 (47)
in Web of Science: 42 (41)
in Scopus: 28 (28)
Cited articles: 62
Citations in Math-Net.Ru: 920
Citations in Web of Science: 19
Citations in Scopus: 251

Number of views:
This page:16911
Abstract pages:37670
Full texts:7362
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:
| by years | by types | by times cited in WoS | by times cited in Scopus | scientific publications | common list |

1. 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: 41)
2. 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: 29)
3. 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: 18)
4. 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: 17)
5. A. G. Baskakov, “On correct linear differential operators”, Sb. Math., 190:3 (1999), 323–348  mathnet  crossref  crossref  mathscinet  zmath  isi  scopus (cited: 17)
6. 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: 16)
7. 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: 15)
8. 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: 13)
9. 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  adsnasa  isi (cited: 14)  elib  scopus (cited: 10)
10. 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: 10)
11. 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  scopus (cited: 9)
12. 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  scopus (cited: 8)
13. A. G. Baskakov, “Linear Relations as Generators of Semigroups of Operators”, Math. Notes, 84:2 (2008), 166–183  mathnet  crossref  crossref  mathscinet  isi  elib  scopus (cited: 7)
14. 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: 7)
15. 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  isi  scopus (cited: 5)
16. A. G. Baskakov, D. M. Polyakov, “Spectral Properties of the Hill Operator”, Math. Notes, 99:4 (2016), 598–602  mathnet  crossref  crossref  mathscinet  isi (cited: 5)  elib  scopus (cited: 5)
17. A. G. Baskakov, V. B. Didenko, “On invertibility states of differential and difference operators”, Izv. Math., 82:1 (2018), 1–13  mathnet  crossref  crossref  adsnasa  isi  elib  scopus (cited: 3)
18. 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  scopus (cited: 3)
19. 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  isi  scopus (cited: 3)
20. A. G. Baskakov, “Fredholm differential and difference operators”, Dokl. Math., 76:2 (2007), 669–672  mathnet  mathscinet  zmath  scopus (cited: 3)
21. 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  scopus (cited: 3)
22. 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  isi  scopus (cited: 2)
23. 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  isi  elib  scopus (cited: 2)
24. 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  scopus (cited: 2)
25. 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: 2)
26. 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  isi  elib  scopus (cited: 1)
27. A. Baskakov, I. Strukova, “Harmonic analysis of functions periodic at infinity”, Eurasian Math. J., 7:4 (2016), 9–29  mathnet (cited: 6)  isi
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, V. V. Obukhovskii, P. Zecca, “On differential inclusions in uniform spaces of functions”, Izv. IMI UdGU, 2006, no. 3(37), 7–8  mathnet
30. 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  scopus
31. A. G. Baskakov, “Estimates of Bounded Solutions of Linear Differential Equations”, Differ. Equ., 39:3 (2003), 447–450  mathnet  crossref  mathscinet
32. A. G. Baskakov, “Splitting of perturbated differential operators with unbounded operator coefficients”, Fundam. Prikl. Mat., 8:1 (2002), 1–16  mathnet  mathscinet  zmath
33. 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
34. 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
35. 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
36. A. G. Baskakov, “Invertibility and the Fredholm property of difference operators”, Math. Notes, 67:6 (2000), 690–698  mathnet  crossref  crossref  mathscinet  zmath  isi
37. 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
38. A. G. Baskakov, “Spectral analysis of linear differential operators, and semigroups of difference operators. I”, Differ. Equ., 33:10 (1997), 1305–1312  mathnet  mathscinet
39. A. G. Baskakov, “Spectral analysis of difference operators with strongly continuous coefficients”, Russian Math. (Iz. VUZ), 41:10 (1997), 1–10  mathnet  mathscinet  zmath
40. 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
41. 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
42. 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
43. A. G. Baskakov, “Spectral analysis of linear differential operators and semigroups of difference operators”, Dokl. Math., 52:1 (1995), 30–32  mathnet  mathscinet  zmath
44. 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
45. 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  isi
46. 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
47. 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
48. A. G. Baskakov, “Some conditions for the invertibility of linear differential and difference operators”, Dokl. Math., 48:3 (1994), 498–501  mathnet  mathscinet  zmath
49. 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
50. 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
51. 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
52. 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
53. 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
54. 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
55. 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
56. 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
57. A. G. Baskakov, “Regularized trace formulas for powers of perturbed spectral operators”, Soviet Math. (Iz. VUZ), 29:8 (1985), 93–96  mathnet  mathscinet  zmath
58. 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
59. A. G. Baskakov, “Harmonic analysis of cosine and exponential operator-valued functions”, Math. USSR-Sb., 52:1 (1985), 63–90  mathnet  crossref  mathscinet  zmath
60. A. G. Baskakov, “Spectral synthesis in Banach modules over commutative Banach algebras”, Math. Notes, 34:4 (1983), 776–782  mathnet  crossref  mathscinet  zmath  isi
61. A. G. Baskakov, “On Ditkin's condition in some Beurling algebras”, Izv. Vyssh. Uchebn. Zaved. Mat., 1982, no. 1, 3–5  mathnet  mathscinet  zmath
62. A. G. Baskakov, “General ergodic theorems in Banach modules”, Funct. Anal. Appl., 14:3 (1980), 215–217  mathnet  crossref  mathscinet  zmath  isi
63. A. G. Baskakov, “Spectral criteria for almost periodicity of solutions of functional equations”, Math. Notes, 24:2 (1978), 606–612  mathnet  crossref  mathscinet  zmath
64. 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  adsnasa  isi
65. 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  isi  scopus
66. 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
67. 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  isi  elib
68. 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

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