Speciality:
01.01.01 (Real analysis, complex analysis, and functional analysis)
Birth date:
22.11.1955
E-mail: ,
Keywords: best approximation; hyperbolic Fourier sum; Kolmogorov width; linear width; best trigonometric approximation; bilinear approximation; trigonometric width; classes of periodic functions.
Subject:
Exact order estimates are obtained of approximation of Besov classes $B^r_{p, \theta}$ of periodic functions of several variables by trigonometric polynomials with harmonics from hyperbolic crosses. The orders are established of Kolmogorov, linear and trigonometric widthes of classes $B^r_{p, \theta}$ in space $L_p$, $1 \leq p, q \leq \infty$. Best $M$-term trigonometric and bilinear approximations of mentioned classes are investigated; in passing some results by Sobolev and Nikolsky in this direction are supplemented and specified. The algorithm is proposed of construction of subspaces of trigonometric polynomials realizing the orders of Kolmogorov widthes of classes of functions of several variables defined by generalized derivative.
Main publications:
A. S. Romanyuk, “Nailuchshie $M$-chlennye trigonometricheskie priblizheniya klassov Besova periodicheskikh funktsii mnogikh peremennykh”, Izv. RAN. Ser. matem., 67:2 (2003), 61–100
A. S. Romanyuk, “Priblizhenie klassov $B_{p,\theta}^r$ periodicheskikh funktsii mnogikh peremennykh lineinymi metodami i nailuchshie priblizheniya”, Matem. sb., 195:2 (2004), 91–116
