Skalyga, Valentin Ivanovich

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Total publications: 22
Scientific articles: 21

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Abstract pages:3602
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Doctor of physico-mathematical sciences (2001)
Speciality: 01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date: 5.01.1947
Keywords: dynamical systems; homotopy invariants in dynamical systems; approximations theory; quadrature formulae; extreme problems of approximations theory; multidimensional analogues of the Markov inequalities for the derivatives of algebraic polynomials.


An effective algorithm for contsructing quadrature formulae, exact on trigonometric polynomials with fixed spectrum was obtained (with S. M. Voronin). The homotopy invariance of local minimum for non-degenerate deformations multicriteria infinite-dimensional mathematics programming problems was proved. Analogues of the V. A. Markov and Schaeffer–Diffin inequalities for algebraic polynomials on convex and centrally symmetric convex bodies was obtained. The best possible estimate for the first derivatives of polynomials on the class convex bounded closed bodies in Banach spaces was established. Exact analogues of the Schaeffer–Duffin inequality on the body bounded by an ellipsoid in Euclidean space was obtained.


Graduated from Faculty of Mathematics of Voronezh State University (VSU) in 1970 (department of functional analysis). Ph.D. thesis was defended in 1984. D.Sci. thesis was defended in 2000. A list of my works contains more than 30 titles.

Main publications:
  • Voronin S. M., Skalyga V. I. O poluchenii algoritmov chislennogo integrirovaniya // Izv. RAN., ser. matem., 1996, 60(5), 13–18.
  • Skalyga V. I. O gomotopicheskom metode v mnogokriterialnykh beskonechnomernykh zadachakh // Izv. RAN, ser. matem., 1997, 61(4), 137–154.
  • Skalyga V. I. Otsenki proizvodnykh polinomov na vypuklykh telakh // Tr. MIAN. 1997, 218, 374–384.
  • Skalyga V. I. Mnogomernye analogi neravenstv V. A. Markova i S. N. Bernshteina // Izv. RAN, ser. matem., 2001, 65(6), 129–172.
List of publications on Google Scholar
List of publications on ZentralBlatt

Publications in Math-Net.Ru
1. V. I. Skalyga, “V. A. Markov's theorems in normed spaces”, Izv. RAN. Ser. Mat., 72:2 (2008),  193–222  mathnet  mathscinet  zmath  elib; Izv. Math., 72:2 (2008), 383–412  isi  scopus
2. V. I. Skalyga, “Analogue of A. A. Markov's inequality for polynomials in two variables”, Mat. Sb., 199:9 (2008),  149–160  mathnet  mathscinet  zmath  elib; Sb. Math., 199:9 (2008), 1409–1420  isi  elib  scopus
3. V. I. Skalyga, “Sharpness conditions in multidimensional analogs of V.  A. Markov's inequality”, Mat. Zametki, 80:6 (2006),  950–953  mathnet  mathscinet  zmath  elib; Math. Notes, 80:6 (2006), 893–897  isi  elib  scopus
4. V. I. Skalyga, “Bounds for the derivatives of polynomials on centrally symmetric convex bodies”, Izv. RAN. Ser. Mat., 69:3 (2005),  179–192  mathnet  mathscinet  zmath  elib; Izv. Math., 69:3 (2005), 607–621  isi  elib  scopus
5. V. I. Skalyga, “Analogs of Markov"s Inequality in Normed Spaces”, Mat. Zametki, 75:5 (2004),  793–796  mathnet  mathscinet  zmath  elib; Math. Notes, 75:5 (2004), 739–743  isi
6. V. I. Skalyga, “Multidimensional analogues of the Markov and Bernstein inequalities”, Izv. RAN. Ser. Mat., 65:6 (2001),  129–172  mathnet  mathscinet  zmath  elib; Izv. Math., 65:6 (2001), 1197–1241  scopus
7. V. I. Skalyga, “Analogs of the Markov and Schaeffer–Duffin inequalities for convex bodies”, Mat. Zametki, 68:1 (2000),  146–150  mathnet  mathscinet  zmath; Math. Notes, 68:1 (2000), 130–134  isi
8. V. I. Skalyga, “Analogues of the Markov and Bernstein inequalities on convex bodies in Banach spaces”, Izv. RAN. Ser. Mat., 62:2 (1998),  169–192  mathnet  mathscinet  zmath; Izv. Math., 62:2 (1998), 375–397  isi  scopus
9. V. I. Skalyga, “On a homotopy method in infinite-dimensional multicriteria problems”, Izv. RAN. Ser. Mat., 61:4 (1997),  137–154  mathnet  mathscinet  zmath; Izv. Math., 61:4 (1997), 813–830  isi  scopus
10. V. I. Skalyga, “Analogues of the Markov and Bernstein inequalities for polynomials in Banach spaces”, Izv. RAN. Ser. Mat., 61:1 (1997),  141–156  mathnet  mathscinet  zmath; Izv. Math., 61:1 (1997), 143–159  isi  scopus
11. V. I. Skalyga, “Estimates for the derivatives of polynomials on convex bodies”, Tr. Mat. Inst. Steklova, 218 (1997),  374–384  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 218 (1997), 372–383
12. N. A. Bobylev, S. K. Korovin, V. I. Skalyga, “A Homotopic Method of Studying Multivalued Problems”, Avtomat. i Telemekh., 1996, 10,  168–178  mathnet  mathscinet  zmath; Autom. Remote Control, 57:10 (1996), 1513–1521
13. S. M. Voronin, V. I. Skalyga, “On numerical integration algorithms”, Izv. RAN. Ser. Mat., 60:5 (1996),  13–18  mathnet  mathscinet  zmath; Izv. Math., 60:5 (1996), 887–891  isi  scopus
14. V. I. Skalyga, “Analogs of an inequality due to the Markov brothers for polynomials on a cube in $\mathbb R^m$”, Mat. Zametki, 60:5 (1996),  783–787  mathnet  mathscinet  zmath; Math. Notes, 60:5 (1996), 589–593  isi
15. V. I. Skalyga, “On deformations of nonsmooth optimization problems having an isolated extremal”, Izv. RAN. Ser. Mat., 58:4 (1994),  186–193  mathnet  mathscinet  zmath; Russian Acad. Sci. Izv. Math., 45:1 (1995), 187–195  isi
16. V. I. Skalyga, “The deformation method for studying nonsmooth infinite-dimensional optimization problems”, Avtomat. i Telemekh., 1993, 11,  66–69  mathnet  mathscinet  zmath; Autom. Remote Control, 54:11 (1993), 1630–1632
17. V. I. Skalyga, “The deformation method for studying infinite-dimensional optimization problems”, Mat. Zametki, 53:2 (1993),  175–176  mathnet  mathscinet  zmath; Math. Notes, 53:2 (1993), 240–241  isi
18. V. I. Skalyga, “On the deformation method for studying the conditional minimum of quality functionals of systems with an infinite number of degrees of freedom”, Avtomat. i Telemekh., 1991, 6,  47–55  mathnet  mathscinet  zmath; Autom. Remote Control, 52:6 (1991), 781–789
19. S. M. Voronin, V. I. Skalyga, “Quadrature formulas”, Dokl. Akad. Nauk SSSR, 276:5 (1984),  1038–1041  mathnet  mathscinet  zmath
20. A. V. Knyazev, V. I. Skalyga, “Matrices of rational differential operators”, Differ. Uravn., 19:10 (1983),  1793–1795  mathnet  mathscinet  zmath
21. V. I. Skalyga, “A follow-up system with coordinate transformation”, Avtomat. i Telemekh., 1982, 2,  169–170  mathnet

22. V. I. Skalyga, “Letter to the Editor”, Mat. Zametki, 77:1 (2005),  156  mathnet  mathscinet  elib; Math. Notes, 77:1 (2005), 146  isi  scopus

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