Skip to main content

Timan’s Type Result on Approximation by Algebraic Polynomials

  • Conference paper

Part of the book series: Operator Theory: Advances and Applications ((OT,volume 98))

Abstract

The paper presents two approximation results of the Jackson-Timan type, which were included in my lecture at the All-Union Conference in Approximation Theory (Dniepropetrovsk, June 26–28, 1990).y1 The conference was dedicated to the seventieth birthday of Professor Alexander Timan (26.6.1920–13.8.1988). Unfortunately, proceedings of the conference never appeared because of the well-known events in the former Soviet Union, and only the abstracts were published (see [B3]). Here we present the approximation method which has been used in the proof of these results. In fact, it can be applied to many other approximation problems of such a kind.

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

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover 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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Yu. A. Brudnyi. Generalization of a theorem of A.F. Timan. Soviet Math. Dokl. 4 (1963), 244–247.

    Google Scholar 

  2. Yu. A. Brudnyi. Approximation of functions by algebraic polynomials, in “Investigations in the contemporary problems of constructive functions theory” (Proceedings of the conference, Baku, October 8–13, 1962), Izdat. AN Azerbajnskoy SSR, Baku, 1968, 40-45 [Russian].

    Google Scholar 

  3. Yu. A. Brudnyi. The A.F. Timan works on algebraic polynomial approximation in Materials of the All-Union Conference in Approximation Theory (Dniepropetrovsk, June 26–29, 1990). Dniepropetrovsk, 1991 13-17 [Russian].

    Google Scholar 

  4. R. Dahlhaus. Pointwise approximation by algebraic polynomials. Journal of Approx. Theory, 57 (1989), 274–277.

    Article  MathSciNet  MATH  Google Scholar 

  5. V.K. Dziadyk. On approximation of function by ordinary polynomials on finite interval of the real line. Jzv. AN SSR, ser. matem. 22 (1958), 351–356 [Russian].

    Google Scholar 

  6. G. Freud. Uber die approximation reelen stetiger Functionen durch gewohnlicke Polinome. Math. Ann. 137 (1959), 17–25.

    Article  MathSciNet  MATH  Google Scholar 

  7. I.E. Gopengauz. A theorem of A.F. Timan on the approximation of functions by polynomials on a finite segment. Mat. Zametki, 1 (1967), 163–172 [Russian].

    MathSciNet  MATH  Google Scholar 

  8. I.E. Gopengauz. Pointwise estimates of the hermitian interpolation. Journal of Approx. Theory 77 (1994), 31–41.

    Article  MathSciNet  MATH  Google Scholar 

  9. S.A. Telyakovskii. Two theorems on approximation of functions by algebraic polynomials, in “American Mathematical Society Translations, Series 2”, 77, 163–177, AMS, Providence, RI, 1966.

    Google Scholar 

  10. A.F. Timan. Improvement of the Jackson theorem on best approximation of continuous functions by polynomials on a finite interval. Soviet Doklady, 78 (1951), 17–20 [Russian].

    MathSciNet  MATH  Google Scholar 

  11. A.F. Timan. Theory of Approximation of Real Functions. Dover Publishers Inc., New-York, 1994.

    Google Scholar 

  12. R.M. Trigub. Approximation of functions by algebraic polynomials with integer coefficients. Jzv. AN SSSR. 26 (1962), 261–280.

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 1997 Springer Basel AG

About this paper

Cite this paper

Brudnyi, Y. (1997). Timan’s Type Result on Approximation by Algebraic Polynomials. In: Gohberg, I., Lyubich, Y. (eds) New Results in Operator Theory and Its Applications. Operator Theory: Advances and Applications, vol 98. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8910-0_6

Download citation

  • DOI: https://doi.org/10.1007/978-3-0348-8910-0_6

  • Publisher Name: Birkhäuser, Basel

  • Print ISBN: 978-3-0348-9824-9

  • Online ISBN: 978-3-0348-8910-0

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics