01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
31.12.1969
E-mail:
Keywords:
integral operators, operators in Hilbert spaces, Kothe spaces, bases, Noetherian operator, eigenfunction, exponential decay, spectrum..
UDC:
517.98, 517.984, 517.984.56, 517.5, 517.988
Subject:
Integral eguation, convolution eguation, geometrical theory of Frechet spaces, spectral operator theory and mathematical physics.
Main publications:
V. M. Kaplitsky, An integral eguation with matrix difference kernel on an interval, Sbornik: Mathematics 198:8 (1998), 1171–1777.
M. A. Kaplitsky, V. M. Kaplitsky, On resolution method for wave problems with some points of change of boundary conditions type. Non-stationary propagation of finite crack of the logitudial shear, Proc. of II Int. Conf. on Modern Problems in Continual Body Mechanics, Rostov-on-Don, 1966, v. 3 (Russian).
V. P. Kondakov, V. M. Kaplitsky, Bases in weighted spaces of entire functions, Linear Topological Spaces and Complex Analysis 3(1997) 85–90.
V. P. Kondakov, V. M. Kaplitsky, On existence of bases in some weighted functional spaces, Geometrical School- Seminar, Abrau-Durso, 1996 (Russian).
V. M. Kaplitsky, Structural guestions of multinormed weighted functional spaces, Diss., Rostov-on-Don, 1998 (Russian).
V. M. Kaplitskii, “A note on asymptotical estimates for the rate of decrease at infinity of the eigenfunctions of integral operators”, Zap. Nauchn. Sem. POMI, 503 (2021), 72–83
2020
2.
V. M. Kaplitskii, “Thermodynamical averages for the Ising model and spectral invariants of Toeplitz matrices”, TMF, 203:3 (2020), 401–416; Theoret. and Math. Phys., 203:3 (2020), 780–793
2018
3.
A. K. Dronov, V. M. Kaplitskii, “On the existence of a basis in a complemented subspace of a nuclear Köthe space from class $(d_1)$”, Mat. Sb., 209:10 (2018), 50–70; Sb. Math., 209:10 (2018), 1463–1481
V. M. Kaplitskii, A. K. Dronov, “To the theory of operators that are bounded on cones in weighted spaces of numerical sequences, II”, Zap. Nauchn. Sem. POMI, 456 (2017), 107–113; J. Math. Sci. (N. Y.), 234:3 (2018), 338–342
2014
5.
V. M. Kaplitskii, “A differential equation for Lerch's transcendent and associated symmetric operators in Hilbert space”, Mat. Sb., 205:8 (2014), 13–40; Sb. Math., 205:8 (2014), 1080–1106
6.
V. M. Kaplitskii, A. K. Dronov, “To the theory of operators that are bounded on cones in weighted spaces of numerical sequences”, Zap. Nauchn. Sem. POMI, 424 (2014), 154–178; J. Math. Sci. (N. Y.), 209:5 (2015), 761–777
V. M. Kaplitskii, “On regulariziers of unbounded linear operators in Banach spaces”, Zap. Nauchn. Sem. POMI, 401 (2012), 93–102; J. Math. Sci. (N. Y.), 194:6 (2013), 651–655
2011
8.
V. M. Kaplitskii, “A method for estimating eigenfunctions of integral operators of certain classes in unbounded domains”, Izv. RAN. Ser. Mat., 75:5 (2011), 65–92; Izv. Math., 75:5 (2011), 933–958
V. M. Kaplitskiĭ, “Asymptotics of the distribution of eigenvalues of a selfadjoint second order hyperbolic differential operator on the two-dimensional torus”, Sibirsk. Mat. Zh., 51:5 (2010), 1041–1060; Siberian Math. J., 51:5 (2010), 830–846
V. M. Kaplitskii, “Asymptotic behaviour of the discrete spectrum of a quasi-periodic
boundary value problem for a two-dimensional hyperbolic equation”, Mat. Sb., 200:2 (2009), 61–74; Sb. Math., 200:2 (2009), 215–228
V. M. Kaplitsky, “Tests for exponential decay of eigenfunctions for some classes of integral operators”, Zap. Nauchn. Sem. POMI, 366 (2009), 53–66; J. Math. Sci. (N. Y.), 165:4 (2010), 455–462
1998
13.
V. M. Kaplitskii, “An integral equation with matrix difference kernel on an interval”, Mat. Sb., 189:8 (1998), 59–66; Sb. Math., 189:8 (1998), 1171–1177
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