Skip to main content
SpringerLink
Log in

Estimate of the norm of the Lagrange interpolation operator in the multidimensional weighted Sobolev space

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

An estimate of the norm of the Lagrange interpolation operator in the multidimensional weighted Sobolev space is obtained. It is shown that, under a certain choice of the sequence of multi-indices, the interpolating polynomials converge to the interpolated function and the rate of convergence is of the order of the best approximation of this function by algebraic polynomials in this space.

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. I. P. Natanson, Constructive Theory of Functions (GITTL, Moscow–Leningrad, 1949) [in Russian].

    Google Scholar 

  2. B. G. Gabdulkhaev, “Approximation in H-spaces and applications,” Dokl. Akad. Nauk SSSR 223 (6), 1293–1296 (1975) [SovietMath. Dokl. 223 (6), 1067–1071 (1976)].

    MathSciNet  MATH  Google Scholar 

  3. B. A. Amosov, “On the approximate solution of elliptic pseudodifferential equations on a smooth closed curve,” Z. Anal. Andwen. 9 (6), 545–563 (1990).

    MathSciNet  MATH  Google Scholar 

  4. B. G. Gabdulkhaev and L. B. Ermolaeva, “The Lagrange interpolation polynomials in Sobolev spaces,” Izv. Vyssh. Uchebn. Zaved. Mat., No. 5, 7–19 (1997) [RussianMath. (Iz. VUZ) 41 (5), 4–16 (1997)].

    MathSciNet  MATH  Google Scholar 

  5. J. Saranen and G. Vainikko, “Fast solvers of integral and pseudodifferential equations on closed curves,” Math. Comp. 67 (224), 1473–1491 (1998).

    Article  MathSciNet  MATH  Google Scholar 

  6. A. I. Fedotov, “An estimate of the norm of the Lagrange interpolation operator in a multidimensional Sobolev space,” Mat. Zametki 81 (3), 427–433 (2007) [Math. Notes 81 (3–4), 373–378 (2007)].

    Article  MathSciNet  MATH  Google Scholar 

  7. A. I. Fedotov, “Convergence of cubature-differencesmethod for multidimensional singular integro-differential equations,” Arch.Math. (Brno) 40 (2), 181–191 (2004).

    MathSciNet  MATH  Google Scholar 

  8. M. Taylor, Pseudodifferential Operators (Princeton University Press, Princeton, NJ; Mir, Moscow, 1985).

    Google Scholar 

  9. I. S. Gradshtein and I. M. Ryzhik, Tables of Integrals, Sums, Series, and Products (Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow, 1963; Academic Press, New York–London, 1965).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kazan Federal University, Kazan, Russia

    A. I. Fedotov

Authors
  1. A. I. Fedotov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. I. Fedotov.

Additional information

Original Russian Text © A. I. Fedotov, 2016, published in Matematicheskie Zametki, 2016, Vol. 99, No. 5, pp. 752–763.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Fedotov, A.I. Estimate of the norm of the Lagrange interpolation operator in the multidimensional weighted Sobolev space. Math Notes 99, 747–756 (2016). https://doi.org/10.1134/S0001434616050126

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S0001434616050126

Keywords

Search

Navigation