01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
5.01.1947
E-mail:
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.
Subject:
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.
Biography
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.
V. I. Skalyga, “Analogue of A. A. Markov's inequality for polynomials in two variables”, Mat. Sb., 199:9 (2008), 149–160; Sb. Math., 199:9 (2008), 1409–1420
V. I. Skalyga, “Sharpness conditions in multidimensional analogs of V. A. Markov's inequality”, Mat. Zametki, 80:6 (2006), 950–953; Math. Notes, 80:6 (2006), 893–897
V. I. Skalyga, “Letter to the editors”, Izv. Math., 69:6 (2005), 1289
5.
V. I. Skalyga, “Bounds for the derivatives of polynomials on centrally symmetric
convex bodies”, Izv. RAN. Ser. Mat., 69:3 (2005), 179–192; Izv. Math., 69:3 (2005), 607–621
V. I. Skalyga, “Multidimensional analogues of the Markov and Bernstein inequalities”, Izv. RAN. Ser. Mat., 65:6 (2001), 129–172; Izv. Math., 65:6 (2001), 1197–1241
V. I. Skalyga, “Analogs of the Markov and Schaeffer–Duffin inequalities for convex bodies”, Mat. Zametki, 68:1 (2000), 146–150; Math. Notes, 68:1 (2000), 130–134
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; Izv. Math., 62:2 (1998), 375–397
V. I. Skalyga, “On a homotopy method in infinite-dimensional multicriteria problems”, Izv. RAN. Ser. Mat., 61:4 (1997), 137–154; Izv. Math., 61:4 (1997), 813–830
11.
V. I. Skalyga, “Analogues of the Markov and Bernstein inequalities for polynomials in Banach spaces”, Izv. RAN. Ser. Mat., 61:1 (1997), 141–156; Izv. Math., 61:1 (1997), 143–159
V. I. Skalyga, “Estimates for the derivatives of polynomials on convex bodies”, Trudy Mat. Inst. Steklova, 218 (1997), 374–384; Proc. Steklov Inst. Math., 218 (1997), 372–383
N. A. Bobylev, S. K. Korovin, V. I. Skalyga, “A Homotopic Method of Studying Multivalued Problems”, Avtomat. i Telemekh., 1996, no. 10, 168–178; Autom. Remote Control, 57:10 (1996), 1513–1521
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; Math. Notes, 60:5 (1996), 589–593
1994
16.
V. I. Skalyga, “On deformations of nonsmooth optimization problems having an isolated extremal”, Izv. RAN. Ser. Mat., 58:4 (1994), 186–193; Russian Acad. Sci. Izv. Math., 45:1 (1995), 187–195
V. I. Skalyga, “The deformation method for studying nonsmooth infinite-dimensional optimization problems”, Avtomat. i Telemekh., 1993, no. 11, 66–69; Autom. Remote Control, 54:11 (1993), 1630–1632
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, no. 6, 47–55; Autom. Remote Control, 52:6 (1991), 781–789