Table of Contents Author Guidelines Submit a Manuscript
Journal of Applied Mathematics
Volume 2012 (2012), Article ID 495054, 9 pages
Research Article

Bernstein Widths of Some Classes of Functions Defined by a Self-Adjoint Operator

School of Mathematics and Information Engineering, Taizhou University, Taizhou 317000, China

Received 9 May 2011; Accepted 2 August 2011

Academic Editor: Kai Diethelm

Copyright © 2012 Guo Feng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. V. M. Tikhomirov, Some Questions in Approximation Theory, Izdat. Moskov. Univ., Moscow, Russia, 1976.
  2. A. Pinkus, n-Widths in Approximation Theory, Springer, New York, NY, USA, 1985.
  3. G. G. Magaril-Il'yaev, “Mean dimension, widths, and optimal recovery of Sobolev classes of functions on the line,” Mathematics of the USSR—Sbornik, vol. 74, no. 2, pp. 381–403, 1993. View at Google Scholar
  4. A. P. Buslaev, G. G. Magaril-Il'yaev, and Nguen T'en Nam, “Exact values of Bernstein widths for Sobolev classes of periodic functions,” Matematicheskie Zametki, vol. 58, no. 1, pp. 139–143, 1995 (Russian). View at Publisher · View at Google Scholar
  5. A. P. Buslaev and V. M. Tikhomirov, “Spectra of nonlinear differential equations and widths of Sobolev classes,” Mathematics of the USSR—Sbornik, vol. 71, no. 2, pp. 427–446, 1992. View at Google Scholar
  6. S. I. Novikov, “Exact values of widths for some classes of periodic functions,” The East Journal on Approximations, vol. 4, no. 1, pp. 35–54, 1998. View at Google Scholar
  7. Nguen Thi Thien Hoa, Optimal quadrature formulae and methods for recovery on function classds defined by variation diminishing convolutions, Candidate's Dissertation, Moscow State University, Moscow, Russia, 1985.
  8. V. A. Jakubovitch and V. I. Starzhinski, Linear Differential Equations with Periodic Coeflicients and Its Applications, Nauka, Moscow, Russia, 1972.
  9. A. Pinkus, “n-widths of Sobolev spaces in Lp,” Constructive Approximation, vol. 1, no. 1, pp. 15–62, 1985. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. K. Borsuk, “Drei Sätze über die n-dimensionale euklidische Sphäre,” Fundamenta Mathematicae, vol. 20, pp. 177–190, 1933. View at Google Scholar · View at Zentralblatt MATH
  11. A. P. Buslaev and V. M. Tikhomirov, “Some problems of nonlinear analysis and approximation theory,” Soviet Mathematics—Doklady, vol. 283, no. 1, pp. 13–18, 1985. View at Google Scholar