Speciality:
01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
23.02.1950
E-mail: Website: https://osipenko.rstu.ru Keywords: approximation theory,
optimal recovery from noisy information,
recovery and approximation of analytic functions,
$n$-widths,
inequalities for derivatives,
quadrature formulas.
Subject:
Optimal recovery methods of analytic functions using the information about exact or inaccurate function values at a fixed system of points were constructed. For the Hardy-Sobolev classes exact values of Kolmogorov $n$-widths, exact constants in Kolmogorov-type inequalities for derivatives, and optimal recovery methods using the information about function values or Fourier coefficients were found. For approximation of analytic functions from Hardy–Sobolev classes an analogue of splines was constructed. Several results concerning optimal recovery of functions and their derivatives on the basis of inaccurate information about their spectrum were obtained.
Main publications:
Osipenko K. Yu., “Exact $n$-widths of Hardy–Sobolev classes”, Constr. Approx., 13 (1997), 17–27
Osipenko K. Yu., Optimal Recovery of Analytic Functions, Nova Science Publishers, Inc., Huntington, New York, 2000
Osipenko K. Yu., “Ob optimalnykh metodakh vosstanovleniya v prostranstvakh Khardi–Soboleva”, Matem. sb., 192:2 (2001), 67–86
Magaril-Ilyaev G. G., Osipenko K. Yu., Tikhomirov V. M., “Optimalnoe vosstanovlenie i teoriya ekstremuma”, Dokl. RAN, 379:2 (2001), 161–164
Osipenko K. Yu., “O nailuchshikh kvadraturnykh formulakh na klassakh Khardi–Soboleva”, Izv. RAN, Ser. matem., 65:5 (2001), 73–90
