Speciality:
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.
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.
