Skip to main content
SpringerLink
Log in

Direct and converse theorems for spline and rational approximation and besov spaces

  • Contributed Papers
  • Conference paper
  • First Online:
Function Spaces and Applications

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1302))

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

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 44.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 59.00
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Bergh, J., J. Löfström, Interpolation spaces, Springer Ver., Grundleren, vol. 223, Berlin, 1976.

    Book  MATH  Google Scholar 

  2. Bergh, J., J. Peetre, On the Spaces Vp (0<p≤∞), Bolletino U.M.I. (4)10 (1974), 632–648.

    MATH  MathSciNet  Google Scholar 

  3. Brudnyi, Yu., Piecewise polynomial approximation and local approximations, Soviet Math. Dokl. 12 (1971) 1591–1594.

    Google Scholar 

  4. Brudnyi, Yu., Spline approximation and functions of bounded variation, Soviet Math. Dokl. 15 (1974), 518–521.

    Google Scholar 

  5. Brudnyi, Yu., Rational approximation and embedding theorems, Doklady AN USSR, 247 (1979), 681–684 (Russian).

    MathSciNet  Google Scholar 

  6. Butzer, P., K. Scherer, Approximationsprozesse und interpolationsmethoden, B.I. Hochschulskripten, Mannheim, 1968.

    MATH  Google Scholar 

  7. Oswald, P., Ungleichunger vom Jackson-Typ für die algebraische beste Approximation in Lp, J. of Approx. Theory 23 (1978) 113–136.

    Article  MATH  MathSciNet  Google Scholar 

  8. Oswald, P., Spline approximation in Lp (0<p<1) metric, Math. Nachr. Bd. 94 (1980), 69–96 (Russian).

    Article  MATH  MathSciNet  Google Scholar 

  9. Peetre, J., New Thoughts on Besov Spaces, Duke Univ. Math. Series, Duke Univ., Durham, 1976.

    MATH  Google Scholar 

  10. Peetre, J., G. Sparr, Interpolation of normed Abelian groups, Ann. Mat. Pura Appl. 92 (1972), 217–262.

    Article  MATH  MathSciNet  Google Scholar 

  11. Pekarski, A., Bernstein type inequalities for the derivatives of rational functions and converse theorems for rational approximation, Math. Sbornik 124(166) (1984), 571–588 (Russian).

    Google Scholar 

  12. Pekarski, A., Classes of analytic functions determined by rational approximation in HP, Math. Sbornik 127(169), (1985), 3–20 (Russian).

    Google Scholar 

  13. Pekarski, A., Estimates for the derivatives of rational functions in LP[−1, 1], Math. Zametki, 39(1986), 388–394 (Russian).

    Google Scholar 

  14. Peller, V., Hankel operators of the calss Gp and their applications (Rational approximation, Gaussian processes, Operator majorant problem), Math. Sbornik 113(155) (1980), 538–582 (Russian).

    MathSciNet  Google Scholar 

  15. Peller, V., Description of Hankel operators of the class σp for p<1, investigation of the order of rational approximation and other applications, Math. Sbornik 122(164) (183), 481–510 (Russian).

    Google Scholar 

  16. Petrushev, P., Relation between rational and spline approximations in Lp metric, J. of Approx. Theory (to appear).

    Google Scholar 

  17. Petrushev, P., Direct and converse theorems for spline approximation and Besov spaces, C.R. Acad. bulg. Sci. 39 (1986), 25–28.

    MATH  MathSciNet  Google Scholar 

  18. Popov, V.A., Direct and converse theorems for spline approximation with free knots, C.R. Acad. bulg. Sci. 26 (1973), 1297–1299.

    MATH  Google Scholar 

  19. Popov, V.A., Direct and converse theorems for spline approximation with free knots in Lp, Rev. Anal. Numér. Théorie Approximation 5 (1976), 69–78.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Mathematics, Bulgarian Academy of Sciences, P.O. Box 373, 1090, Sofia, Bulgaria

    Pencho P. Petrushev

Authors
  1. Pencho P. Petrushev
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Michael Cwikel Jaak Peetre Yoram Sagher Hans Wallin

Rights and permissions

Reprints and permissions

Copyright information

© 1988 Springer-Verlag

About this paper

Cite this paper

Petrushev, P.P. (1988). Direct and converse theorems for spline and rational approximation and besov spaces. In: Cwikel, M., Peetre, J., Sagher, Y., Wallin, H. (eds) Function Spaces and Applications. Lecture Notes in Mathematics, vol 1302. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0078887

Download citation

  • DOI: https://doi.org/10.1007/BFb0078887

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-18905-3

  • Online ISBN: 978-3-540-38841-8

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation