Skip to main content
SpringerLink
Log in

On the Limits of Lagrange Projectors

  • Published:
Constructive Approximation Aims and scope

Abstract

This article addresses a question of Carl de Boor (In: Constructive theory of functions, Varna 2005, pp. 51–63, Marin Drinov Academic, Sofia, [2006]): What ideal projectors are the limits of Lagrange projectors? The results of this paper answer the question in the sense that for every ideal projector P, we prescribe finitely many computations that determine whether the projector P is a limit of Lagrange projectors.

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. Birkhoff, G.: The algebra of multivariate interpolation. In: Coffman, C.V., Fix, G.J. (eds.) Constructive Approaches to Mathematical Models, pp. 345–363. Academic Press, New York (1979)

    Google Scholar 

  2. de Boor, C.: Ideal interpolation. In: Chui, C.K., Neamtu, M., Schumaker, L. (eds.) Approximation Theory XI, Gatlinburg 2004, pp. 59–91. Nashboro Press, Brentwood (2005)

    Google Scholar 

  3. de Boor, C.: What are the limits of Lagrange projectors? In: Bojanov, B. (ed.) Constructive Theory of Functions, Varna 2005, pp. 51–63. Marin Drinov Academic, Sofia (2006)

    Google Scholar 

  4. Cox, D., Little, J., O’Shea, D.: Ideals, Varieties, and Algorithms, 2nd edn. Springer, New York (1997)

    Google Scholar 

  5. Cox, D., Little, J., O’Shea, D.: Using Algebraic Geometry, Graduate Texts in Mathematics. Springer, New York (1998)

    Google Scholar 

  6. Iarrobino, A.: Reducibility of the families of 0-dimensional schemes on a variety. Invent. Math. 15, 72–77 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  7. Mumford, D.: The Red Book of Varieties and Schemes. Lecture Notes in Mathematics, vol. 1358. Springer, Berlin (1988)

    MATH  Google Scholar 

  8. Shekhtman, B.: On a conjecture of Carl de Boor regarding the limits of Lagrange interpolants. Constr. Approx. 24(3), 365–370 (2006)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of South Florida, Tampa, FL, 33620, USA

    Boris Shekhtman

Authors
  1. Boris Shekhtman
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Boris Shekhtman.

Additional information

Communicated by Carl de Boor.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Shekhtman, B. On the Limits of Lagrange Projectors. Constr Approx 29, 293–301 (2009). https://doi.org/10.1007/s00365-008-9016-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00365-008-9016-0

Keywords

Mathematics Subject Classification (2000)

Search

Navigation