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Strelkov, Nikolay Aleksandrovich
Professor
Doctor of physico-mathematical sciences (1993)
Birth date: 04.08.1947
E-mail:
Keywords: optimality, wavelets, splines, projection-net approximation, widths, packings, coverings, tilings, finite element methods.

Subject:

The main research directions: approximation in functional spaces, numerical methods, wavelets. Method of investigation is the synthesis of numerical analysis, theory of functions and geometrical number theory. 1) The approximation properties of subspaces generated by translations on a lattice of fixed function: a) definition of projection-net widths describing the approximation properties of such subspaces; b) the relationship between these widths and geometrical properties of Lebesgue sets packings; c) necessary and sufficient conditions for the optimality and the construction of optimal subspaces; d) the definition of average dimension and the comparison of projection-net and Kolmogorov widths of the same average dimension; e) direct and inverse projection-net theorems. 2) Wavelets: a) construction of wavelet bases which are universally optimal for the whole scale of Sobolev spaces; b) the constructive description of wavelets generated by some n-dimensional lattice tilings; c) the investigation of relationship between B–splines and wavelets; d) construction of the family of biorthonormal wavelet bases with compact supports; e) the calculation of exact constants for spline inequalities. 3) The investigation of the family of spline-trigonometrical bases: a) construction of biorthonormal pair of functional systems such that functions of the first system are the productions of trigonometrical and algebraical polinomials and functions of the second system are the productions of trigonometrical polinomials and derivatives of Schoenberg B–splines; b) interpolate representations of the entire functions of exponential type based on the using of spline-trigonometrical bases (these representations are similar to the well-known Shannon–Kotel"nikov theorem); c) construction and investigation of projection-difference analogs of differential operators by means of representations of the entire functions of exponential type; d) consideration of asymptotical behaviour of spline-trigonometrical bases generating some new integral transforms; e) the investigation of Lebesgue functions and constants for these bases. 4) Difference and finite-element approximation: a) the necessary and sufficient conditions of coincidence of difference and finite element operators; b) the complete description of the family of coordinate functions with asymptotically optimal approximative properties which generate the projection-difference approximations of n–dimensional Laplace operator coinciding with its simplest difference (2n+1)–point "cross-type" analog; c) the projection-net and difference approximations of Laplacian using wide-spaced nets.

Biography

Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 1970 (department of computional mathematics). Ph.D. thesis was defended in 1973. D.Sci. thesis was defended in 1993. A list of my works contains more than 100 titles.
   
Main publications:
  • Strelkov N. A. Proektsionno-setochnye poperechniki i reshetchatye ukladki // Matem. sbornik, 1991, 182(10), 1513–1533.
  • Strelkov N. A. Ermitovy poperechniki, srednyaya razmernost i kratnye ukladki // Matem. sbornik, 1996, 187(1), 121–142.
  • Strelkov N. A. Proektsionno-setochnye analogi operatora Laplasa tipa "krest" // Zhurn. vychislit. matem. i matem. fiz., 1996, 36(10), 46–55.
  • Strelkov N. A. Universalno optimalnye vspleski // Matem. sbornik, 1997, 188(1), 147–160.
  • Strelkov N. A. Splain-trigonometricheskie bazisy i ikh svoistva // Matem. sbornik, 2001, 192(7), 125–160.

https://www.mathnet.ru/eng/person8409
List of publications on Google Scholar
https://mathscinet.ams.org/mathscinet/MRAuthorID/281793

Publications in Math-Net.Ru Citations
2018
1. A. A. Korotkin, A. A. Maksimov, N. A. Strelkov, “On one problem of calculating a two-dimensional convolution with an exponential kernel”, Zh. Vychisl. Mat. Mat. Fiz., 58:11 (2018),  1771–1779  mathnet  elib; Comput. Math. Math. Phys., 58:11 (2018), 1708–1715  isi  scopus
2001
2. N. A. Strelkov, “Spline trigonometric bases and their properties”, Mat. Sb., 192:7 (2001),  125–160  mathnet  mathscinet  zmath; Sb. Math., 192:7 (2001), 1053–1088  isi  scopus 2
1997
3. N. A. Strelkov, “Universally optimal wavelets”, Mat. Sb., 188:1 (1997),  147–160  mathnet  mathscinet  zmath; Sb. Math., 188:1 (1997), 157–171  isi  scopus 1
1996
4. N. A. Strelkov, “Hermitian widths, mean dimension, and multiple packings”, Mat. Sb., 187:1 (1996),  121–142  mathnet  mathscinet  zmath; Sb. Math., 187:1 (1996), 119–139  isi  scopus 1
5. N. A. Strelkov, “Cross-type projection-grid analogues of the Laplace operator”, Zh. Vychisl. Mat. Mat. Fiz., 36:10 (1996),  46–55  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 36:10 (1996), 1359–1366  isi
1995
6. N. A. Strelkov, “Direct and inverse finite difference projection methods”, Mat. Zametki, 57:4 (1995),  586–596  mathnet  mathscinet  zmath  elib; Math. Notes, 57:4 (1995), 407–413  isi 1
1994
7. N. A. Strelkov, “Local approximation of projection-difference methods”, Zh. Vychisl. Mat. Mat. Fiz., 34:2 (1994),  201–213  mathnet  mathscinet  zmath; Comput. Math. Math. Phys., 34:2 (1994), 165–174  isi 1
1992
8. N. A. Strelkov, “Criterion for the asymptotic optimality of projection-grid subspaces”, Mat. Zametki, 52:4 (1992),  89–98  mathnet  mathscinet  zmath; Math. Notes, 52:4 (1992), 1051–1057  isi
1991
9. N. A. Strelkov, “Projection-net widths and lattice packings”, Mat. Sb., 182:10 (1991),  1513–1533  mathnet  mathscinet  zmath; Math. USSR-Sb., 74:1 (1993), 251–269  isi 6
1989
10. N. A. Strelkov, “Optimal coordinate functions in projection-difference methods, widths and lattice packings”, Dokl. Akad. Nauk SSSR, 309:3 (1989),  550–554  mathnet  mathscinet  zmath; Dokl. Math., 40:3 (1990), 558–562 2
1982
11. N. A. Strelkov, “Spline-trigonometric bases in $L_2$ and interpolation of entire functions of exponential type”, Mat. Zametki, 32:6 (1982),  835–840  mathnet  mathscinet  zmath; Math. Notes, 32:6 (1982), 905–908  isi 1
1981
12. N. A. Strelkov, “Projection-difference analogs of the Laplace operator”, Zh. Vychisl. Mat. Mat. Fiz., 21:5 (1981),  1326–1328  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 21:5 (1981), 254–257 2
1979
13. N. A. Strelkov, “Iterative methods for solving linear and quasilinear projection-difference analogs of fourth-order boundary-value problems”, Zh. Vychisl. Mat. Mat. Fiz., 19:1 (1979),  143–155  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 19:1 (1979), 147–160
1977
14. N. A. Strelkov, “The choice of coordinate functions in projection-difference methods”, Zh. Vychisl. Mat. Mat. Fiz., 17:6 (1977),  1443–1457  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 17:6 (1977), 100–113 2
1973
15. N. A. Strelkov, “On approximations of certain function spaces and their applications”, Dokl. Akad. Nauk SSSR, 209:3 (1973),  565–568  mathnet  mathscinet  zmath
1971
16. N. A. Strelkov, “Simplicial extensions of network functions and their application to the solution of problems of mathematical physics”, Zh. Vychisl. Mat. Mat. Fiz., 11:4 (1971),  969–981  mathnet  mathscinet  zmath; U.S.S.R. Comput. Math. Math. Phys., 11:4 (1971), 190–204 1

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