Skip to main content
SpringerLink
Log in

Optimal recovery of the Sobolev-Wiener class of smooth functions by double sampling

  • Published:
Constructive Approximation Aims and scope

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

An optimal interpolation problem is considered on the Sobolev-Wiener class of smooth functions defined on the real line by double samples. We calculate the exact value of the minimal intrinsic error, identify an optimal set of sampling points and constructing an optimal linear estimator (algorithm).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. A. S. Cavaretta Jr. (1974):An elementary proof of Kolmogorov's inequality. Amer. Math. Monthly,5:480–486.

    Google Scholar 

  2. J. J. F. Fournier, J. Stewart (1985):Amalgams of L p and l q. Bull. Amer. Math. Soc.,13(1):1–20.

    Google Scholar 

  3. Daren Huang, Yongsheng Sun (1988):Optimal interpolation on some classes of differentiable functions. ATA,4(3):13–22.

    Google Scholar 

  4. A. A. Ligun (1985):Exact inequalities for perfect splines and its applications (in Russian). Izv. Vyssh. Uchben. Zaved. Mat.,5:32–38.

    Google Scholar 

  5. Yongping Liu (to appear):Infinite-dimensional widths and optimal recovery of some smooth function classes of L p (R)in metric L(R).

  6. Yongping Liu, Yongsheng Sun (1992):Infinite-dimensional width and optimal interpolation problems on Sobolev-Wiener space. Sci. Sinica Ser. A,6:582–591.

    Google Scholar 

  7. V. P. Motornyi (1974):On the best quadrature formula of the form Σp k f(x k )for some classes of differentiable periodic functions (in Russian). Izv. Akad. Nauk SSSR Ser. Mat.,38(3):583–614.

    Google Scholar 

  8. Yongsheng Sun (1991):Optimal interpolation on some classes of smooth functions defined on the whole real axis. Adv. in Math. (in Chinese),20(1):1–14.

    Google Scholar 

  9. Yongsheng Sun (1986):Optimal recovery on some classes of differentiable functions. ATA,2(4):49–54.

    Google Scholar 

  10. Yongsheng Sun (1986):Optimal recovery on some classes of differentiable functions. Kexue Tongbao (Bull. of Sciences, in Chinese),11:809–812.

    Google Scholar 

  11. Yongsheng Sun (1989): Theory of Approximation, vol. 1 (in Chinese). Beijing: Beijing Normal University Press.

    Google Scholar 

  12. Yongsheng Sun, Daren Huang (1986):Optimal interpolation on some classes of differentiable functions. In: Approximation Theory, V (C. K. Chui et al., eds.). New York: Academic Press.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Beijing Normal University, 100875, Beijing, The People's Republic of China

    Yongsheng Sun & Yongping Liu

Authors
  1. Yongsheng Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Yongping Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Communicated by Charles A. Micchelli.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sun, Y., Liu, Y. Optimal recovery of the Sobolev-Wiener class of smooth functions by double sampling. Constr. Approx 9, 391–405 (1993). https://doi.org/10.1007/BF01204648

Download citation

  • Received:

  • Revised:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01204648

AMS classification

Key words and phrases

Search

Navigation