01.01.02 (Differential equations, dynamical systems, and optimal control)
Birth date:
19.10.1965
E-mail:
Keywords:
Ordinary differential operators, Schrödinger operator, convergence of spectral expansions, eigen and associated functions, basis properties, boundary control, differential operators with involution
Subject:
Spectral theory of differential operators, boundary control theory
Main publications:
V. A. Il'in, L. V. Kritskov, “Properties of spectral expansions corresponding to non-self-adjoint differential operators”, Journal of Mathematical Sciences, 116:5 (2003), 3489–3550
L. V. Kritskov, “O zadachakh granichnogo upravleniya dlya uravneniya Kleina-Gordona-Foka s summiruemym koeffitsientom”, Differentsialnye uravneniya, 51:5 (2015), 688–696
L. V. Kritskov, “Ravnomernaya na vsei pryamoi skhodimost spektralnogo razlozheniya dlya operatora Shredingera s potentsialom-raspredeleniem”, Differentsialnye uravneniya, 53:2 (2017), 183–194
L. V. Kritskov, “Otsenka prirascheniya spektralnoi funktsii operatora Shredingera s potentsialom, udovletvoryayuschim usloviyu tipa Kato”, Differentsialnye uravneniya, 35:8 (1999), 1077–1086
L. V. Kritskov, A. M. Sarsenbi, “Bazisnost Rissa sistemy kornevykh funktsii differentsialnogo operatora vtorogo poryadka s involyutsiei”, Differentsialnye uravneniya, 53:1 (2017), 35–48
L. V. Kritskov, “Uniform, on the real line, equiconvergence of spectral expansions for the higher-order differential operators”, Dokl. Math., 101:2 (2020), 132–134
2018
2.
L. V. Kritskov, D. Yu. Borodinova, “Estimates of the root functions of a one-dimensional Schrödinger operator with a strong boundary singularity”, Differential Equations, 54:5 (2018), 567–577
3.
L. V. Kritskov, A. M. Sarsenbi, “Equiconvergence property for spectral expansions related to perturbations of the operator $-u(-x)$ with initial data”, Filomat, 32:3 (2018), 1069–1078 (to appear)
L. V. Kritskov, “Bessel property of the system of root functions of a second-order singular operator on an interval”, Differential Equations, 54:8 (2018), 1032–1048
5.
L. V. Kritskov, M. A. Sadybekov, A. M. Sarsenbi, “Nonlocal spectral problem for a second-order differential operator with an involution”, Bulletin of the Karaganda University - Mathematics, 2018, no. 3 (91), 53–60http://mathematics-vestnik.ksu.kz/apart/2018-91-3/6.pdf
L. V. Kritskov, “Classes of uniform convergence of spectral expansions for the one-dimensional Schrödinger operator with a distribution potential”, Differential Equations, 53:5 (2017), 583–594
7.
L. V. Kritskov, “Uniform, on the entire axis, convergence of the spectral expansion for Schrödinger operator with a potential-distribution”, Differential Equations, 53:2 (2017), 180–191
8.
L. V. Kritskov, A. M. Sarsenbi, “Riesz basis property of system of root functions of second-order differential operator with involution”, Differential Equations, 53:1 (2017), 33–46
9.
L. V. Kritskov, “Estimates for Root Functions of a Singular Second-Order Differential Operator”, Functional Analysis in Interdisciplinary Applications. FAIA 2017., Springer Proceedings in Mathematics & Statistics, 216, eds. T. S. Kalmenov , E. D. Nursultanov, M. V. Ruzhansky, M. A. Sadybekov, Springer, Cham, 2017, 245–257
D. V. Goryashin, A. S. Zelenskii, A. I. Kozko, L. V. Kritskov, V. S. Panferov, A. G. Razborov, I. N. Sergeev, I. A. Sheipak, M. V. Yumashev, Kvant, 2017, no. 9, 53–55
11.
D. V. Goryashin, A. S. Zelenskii, A. I. Kozko, L. V. Kritskov, V. S. Panferov, A. G. Razborov, I. N. Sergeev, I. A. Sheipak, M. V. Yumashev, S. S. Chesnokov, Kvant, 2017, no. 4, 52–58
2015
12.
L. V. Kritskov, A. M. Sarsenbi, “Basicity in $L_p$ of root functions for differential equations with involution”, Electronic Journal of Differential Equations, 2015:278 (2015) , 9 pp.
13.
L. V. Kritskov, A. M. Sarsenbi, “Spectral properties of a nonlocal problem for a second-order differential equation with an involution”, Differential Equations, 51:8 (2015), 984–990
14.
L. V. Kritskov, “On boundary control problems for the Klein-Gordon-Fock equation with an integrable coefficient”, Differential Equations, 51:5 (2015), 701–709
15.
L. V. Kritskov, “Necessary condition for the uniform minimality of Kostyuchenko type systems”, Azerbaijan Journal of Mathematics, 5:1 (2015), 97–103
2013
16.
M. F. Abdukarimov, L. V. Kritskov, “Boundary control problem for the one-dimensional Klein-Gordon-Fock equation with a variable coefficient: the case of control by displacements at two endpoints”, Differential Equations, 49:8 (2013), 1006–1017
17.
M. F. Abdukarimov, L. V. Kritskov, “Boundary control of the displacement at one end with the other end free for a process described by the telegraph equation with a variable coefficient”, Doklady Mathematics, 87:3 (2013), 351–353
18.
M. F. Abdukarimov, L. V. Kritskov, “Boundary control problem for the one-dimensional Klein-Gordon-Fock equation with a variable coefficient. The case of control by displacement at one endpoint with the other endpoint being fixed”, Differential Equations, 49:6 (2013), 731–743
2003
19.
V. A. Il'in, L. V. Kritskov, “Properties of spectral expansions corresponding to non-self-adjoint differential operators”, J. Math. Sci. (N. Y.), 116:5 (2003), 3489–3550
2000
20.
L. V. Kritskov, “Estimates of generalized eigenfunctions of two-term differential operator of even order”, Differ. Equ., 36:10 (2000), 1443–1451
1999
21.
L. V. Kritskov, “An estimate for the increment of the spectral function of the Schrödinger operator with a potential satisfying a Kato-type condition”, Differ. Equ., 35:8 (1999), 1087–1097
22.
L. V. Kritskov, “An estimate for Fourier images in a system of generalized eigenfunctions of the Schrödinger operator with a Stummel-type potential”, Math. Notes, 65:4 (1999), 454–461
1998
23.
L. V. Kritskov, “On spectral expansions corresponding to the multidimensional Schrödinger operator with summable potential. II”, Differ. Equ., 34:10 (1998), 1376–1385
24.
L. V. Kritskov, “On spectral expansions corresponding to the multidimensional Schrödinger operator with a summable potential. I”, Differ. Equ., 34:5 (1998), 610–620
1997
25.
L. V. Kritskov, “A lower bound for the Fourier images in the system of fundamental functions of the one-dimensional Schrödinger operator with a summable potential”, Differ. Equ., 33:10 (1997), 1327–1334
26.
L. V. Kritskov, “On the ordered spectral representation of the space $L_2(\mathbf R)$ with respect to the Stark-effect Hamiltonian of regular type. II”, Differ. Equ., 33:3 (1997), 348–354
1996
27.
L. V. Kritskov, “On the ordered spectral representation of the space $L_2(\mathbf R)$ with respect to the Stark-effect Hamiltonian of regular type. I”, Differ. Equ., 32:12 (1996), 1592–1600
28.
L. V. Kritskov, “On an ordered spectral representation of the space $L_2$ with respect to the Schrödinger operator with a singular matrix potential”, Differ. Equ., 32:5 (1996), 631–639
29.
L. V. Kritskov, “Distribution of eigenvalues for uniformly minimal systems of root functions of ordinary differential operators”, Differ. Equ., 32:1 (1996), 64–72
30.
V. A. Il'in, L. V. Kritskov, “An estimate, uniform on the whole line $\mathbb R$, for the rate of convergence of a spectral expansion corresponding to the Schrödinger operator with a summable potential”, Differ. Equ., 32:1 (1996), 32–37
31.
L. V. Kritskov, “To the problem on the basis property of the system $\{\exp(iant) \sin(nt)\}$”, Doklady Mathematics, 53:1 (1996), 33–34
1995
32.
L. V. Kritskov, “Analytic description of an ordered spectral representation of the space $L_2(\mathbf R^N)$ with respect to a Schrödinger operator with a potential in the Kato class”, Differ. Equ., 31:12 (1995), 2008–2015
33.
V. A. Il'in, L. V. Kritskov, “An estimate for the spectral function of the one-dimensional Stark-effect Hamiltonian”, Differ. Equ., 31:9 (1995), 1409–1418
34.
V. A. Il'in, L. V. Kritskov, “An estimate that is uniform on the whole line for generalized eigenfunctions of the one-dimensional Schrödinger operator with a uniformly locally summable potential”, Differ. Equ., 31:8 (1995), 1267–1274
35.
L. V. Kritskov, “Boundedness of the multiplicities for the systems of generalized exponents that are uniformly minimal in $L_2$”, Doklady Mathematics, 51:2 (1995), 231–232
1993
36.
L. V. Kritskov, “Distribution of the eigenvalues of singular differential operators on an interval”, Differ. Equ., 29:5 (1993), 660–665
37.
L. V. Kritskov, “Representation and estimates of root functions of singular differential operators on an interval. II”, Differ. Equ., 29:1 (1993), 54–61
1992
38.
L. V. Kritskov, “Representation and estimates of root functions of singular differential operators on an interval. I”, Differ. Equ., 28:8 (1992), 1035–1045
1991
39.
L. V. Kritskov, “The unconditional basis property for systems of root functions of the one-dimensional singular Schrödinger operator”, Differ. Uravn., 27:8 (1991), 1446–1447
1990
40.
L. V. Kritskov, “On necessary conditions for the basis property in $L_p(G)$ of a system of root functions of the one-dimensional Schrödinger operator”, Soviet Math. Doklady, 41:2 (1990), 374–377
41.
L. V. Kritskov, Nekotorye spektralnye svoistva singulyarnykh obyknovennykh differentsialnykh operatorov vtorogo poryadka, Diss. … kand. fiz.-matem. nauk, MGU, Moskva, 1990 , 148 pp.
1989
42.
L. V. Kritskov, “A uniform estimate for the order of associated functions, and the distribution of eigenvalues of a one-dimensional Schrödinger operator”, Differ. Equ., 25:7 (1989), 784–791
2020
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