The problem of uniquiness of multiple Walsh series was solved; the problem of a.e. convergence of multiple Walsh series of integrable functions was solved; the problem of convergence of multiple Walsh series in measure and in near to L Orlicz space was solved.
Biography
Graduated from Faculty of Mathematics and Mechanics of N. G. Chernyshevsky Saratov State University in 1965 (department of analysis mathematical). Ph.D. thesis was defended in 1975. D.Sci. thesis was defended in 1998. A list of my works contains more than 50 titles.
Main publications:
Lukomskii S. F. On a U-set for multiple Walsh series // Analysis Mathematica. 1992. V. 18, no. 2. P. 127–138.
Lukomskii S. F. Convergence of multiple Walsh series in measure and in L // East Journal on Approximations. 1997. V. 3, no. 3. P. 101–116.
Lukomskii S. F. Convergence of multiple Walsh series in near to L Orlicz space // East Journal on Approximations. 2000. V. 6, no. 3. P. 295–308.
S. F. Lukomskii, Iu. S. Kruss, “Unitary extension principle on zero-dimensional locally compact groups”, Izv. Saratov Univ. Math. Mech. Inform., 23:3 (2023), 320–338
2021
2.
S. F. Lukomskii, D. S. Lukomskii, “Numerical solution of linear differential equations with discontinuous coefficients and Henstock integral”, Izv. Saratov Univ. Math. Mech. Inform., 21:2 (2021), 151–161
3.
S. F. Lukomskii, “On the Uniqueness Sets of Multiple Walsh Series for Convergence in Cubes”, Mat. Zametki, 109:3 (2021), 397–406; Math. Notes, 109:3 (2021), 427–434
S. F. Lukomskii, M. D. Mushko, “On binary B-splines of second order”, Izv. Saratov Univ. Math. Mech. Inform., 18:2 (2018), 172–182
5.
S. F. Lukomskii, P. A. Terekhin, S. A. Chumachenko, “Rademacher Chaoses in Problems of Constructing Spline Affine Systems”, Mat. Zametki, 103:6 (2018), 863–874; Math. Notes, 103:6 (2018), 919–928
S. F. Lukomskii, A. M. Vodolazov, “Fast discrete Fourier transform on local fields of positive characteristic”, Probl. Peredachi Inf., 53:2 (2017), 60–69; Problems Inform. Transmission, 53:2 (2017), 155–163
A. M. Vodolazov, S. F. Lukomskii, “Shift systems in local fields of zero characteristic”, Zap. Nauchn. Sem. POMI, 455 (2017), 25–32; J. Math. Sci. (N. Y.), 234:2 (2018), 130–134
2016
8.
A. M. Vodolazov, S. F. Lukomskii, “Orthogonal shift systems in the field of $p$-adic numbers”, Izv. Saratov Univ. Math. Mech. Inform., 16:3 (2016), 256–262
D. S. Lukomskii, S. F. Lukomskii, P. A. Terekhin, “Solution of Cauchy problem for equation first order via Haar functions”, Izv. Saratov Univ. Math. Mech. Inform., 16:2 (2016), 151–159
S. F. Lukomskii, G. S. Berdnikov, Yu. S. Kruss, “On the Orthogonality of a System of Shifts of the Scaling Function on Vilenkin Groups”, Mat. Zametki, 98:2 (2015), 310–313; Math. Notes, 98:2 (2015), 339–342
A. A. Baryshev, D. S. Lukomskii, S. F. Lukomskii, “Systems of Scales and Shifts in the Problem Still Image Compression”, Izv. Saratov Univ. Math. Mech. Inform., 14:4(2) (2014), 505–510
S. F. Lukomskii, “Matrix representation of dilation operator on the product of zero-dimensional locally compact Abelian groups”, Izv. Saratov Univ. Math. Mech. Inform., 13:2(1) (2013), 8–14
2011
15.
S. F. Lukomskii, “Nonorthogonal multiresolution analysis on zero-dimensional locally compact groups”, Izv. Saratov Univ. Math. Mech. Inform., 11:3(1) (2011), 25–32
S. F. Lukomskii, “Multiresolution analysis on zero-dimensional Abelian groups and wavelets bases”, Mat. Sb., 201:5 (2010), 41–64; Sb. Math., 201:5 (2010), 669–691
S. F. Lukomskii, “Fourier series of functions with a non-summable derivative”, Izv. RAN. Ser. Mat., 73:2 (2009), 91–108; Izv. Math., 73:2 (2009), 301–318
S. F. Lukomskii, “$\Lambda(\Psi)$-Fluctuation and the Fourier-Walsh series of bounded functions”, Sibirsk. Mat. Zh., 48:4 (2007), 811–816; Siberian Math. J., 48:4 (2007), 648–652
21.
S. F. Lukomskii, “The Fourier–Walsh series of the functions absolutely continuous in the generalized restricted sense”, Sibirsk. Mat. Zh., 48:2 (2007), 341–352; Siberian Math. J., 48:2 (2007), 273–282
S. F. Lukomskii, “On subsequences of partial sums of Fourier-Walsh series in Lorentz spaces”, Izv. Vyssh. Uchebn. Zaved. Mat., 2006, no. 6, 48–55; Russian Math. (Iz. VUZ), 50:6 (2006), 46–53
Yu. V. Kupriyanova, S. F. Lukomskiy, “Оn optimal choice of interpolation spline on triangular net”, Izv. Saratov Univ. Math. Mech. Inform., 5:1-2 (2005), 26–33
S. F. Lukomskii, “On the coefficients of lacunary trigonometric series and Rademacher series that converge to sets of measure zero”, Izv. Vyssh. Uchebn. Zaved. Mat., 1995, no. 9, 37–47; Russian Math. (Iz. VUZ), 39:9 (1995), 35–45
26.
S. F. Lukomskii, “A criterion for the almost-everywhere convergence of Fourier–Walsh square partial sums of integrable functions”, Mat. Sb., 186:7 (1995), 133–146; Sb. Math., 186:7 (1995), 1057–1070
S. F. Lukomskii, “Divergence almost everywhere of square partial sums of Fourier–Walsh series of integrable functions”, Mat. Zametki, 56:1 (1994), 57–62; Math. Notes, 56:1 (1994), 690–693
S. F. Lukomskii, “On certain classes of sets of uniqueness of multiple Walsh series”, Mat. Sb., 180:7 (1989), 937–945; Math. USSR-Sb., 67:2 (1990), 393–401
S. F. Lukomskii, “Necessary conditions for sets of uniqueness of Walsh series with
gaps”, Mat. Sb. (N.S.), 133(175):4(8) (1987), 469–480; Math. USSR-Sb., 61:2 (1988), 461–470
S. F. Lukomskiĭ, “Walsh series with gaps”, Izv. Vyssh. Uchebn. Zaved. Mat., 1985, no. 12, 16–19; Soviet Math. (Iz. VUZ), 29:12 (1985), 19–23
1974
32.
S. F. Lukomskii, “Singularities of carleman type for subsystems of a trigonometric system”, Mat. Zametki, 15:4 (1974), 515–520; Math. Notes, 15:4 (1974), 301–304
Presentations in Math-Net.Ru
1.
Аппроксимация жесткими фреймами в нуль-мерных группах S. F. Lukomskii, A. M. Vodolazov XXII International Saratov Winter School
"Contemporary Problems of Function Theory and Their Applications",
dedicated to the 300th anniversary of the Russian Academy of Sciences January 29, 2024 16:00
Tight wavelet frames in zero dimensional groups S. F. Lukomskii International Conference "Approximation Theory and Applications" Dedicated to the 100th Anniversary S. B. Stechkin September 8, 2021 16:40
Trees in MRA on Vilenkin groups S. F. Lukomskii International conference "Nonlinear Approximations and Applications" dedicated to the 60th birthday of Professor V. N. Temlyakov October 31, 2013 17:15
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