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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Yu. A. Brudnyi. Generalization of a theorem of A.F. Timan. Soviet Math. Dokl. 4 (1963), 244–247.
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].
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].
R. Dahlhaus. Pointwise approximation by algebraic polynomials. Journal of Approx. Theory, 57 (1989), 274–277.
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].
G. Freud. Uber die approximation reelen stetiger Functionen durch gewohnlicke Polinome. Math. Ann. 137 (1959), 17–25.
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].
I.E. Gopengauz. Pointwise estimates of the hermitian interpolation. Journal of Approx. Theory 77 (1994), 31–41.
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.
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].
A.F. Timan. Theory of Approximation of Real Functions. Dover Publishers Inc., New-York, 1994.
R.M. Trigub. Approximation of functions by algebraic polynomials with integer coefficients. Jzv. AN SSSR. 26 (1962), 261–280.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights 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