A. G. Babenko, M. V. Deikalova, S. G. Revesz, “Weighted one-sided approximation of characteristic functions of intervals by polynomials on a closed interval”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 4, 2015, 46–53; Proc. Steklov Inst. Math. (Suppl.), 297, suppl. 1 (2017), 11

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Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2015, Volume 21, Number 4, Pages 46–53 (Mi timm1228)

This article is cited in 4 scientific papers (total in 4 papers)

Weighted one-sided approximation of characteristic functions of intervals by polynomials on a closed interval

A. G. Babenko^ab, M. V. Deikalova^ab, S. G. Revesz^c

^a Institute of Mathematics and Computer Science, Ural Federal University, Ekaterinburg
^b Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
^c Alfréd Rényi Institute of Mathematics, Hungary Academy of Sciences

Full-text PDF (188 kB) Citations (4)

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Abstract: We consider the problem of weighted one-sided approximation on the interval

[- 1, 1]

$[-1,1]$ of characteristic functions of intervals

(a, 1] \subset (- 1, 1]

$(a,1]\subset(-1,1]$ and

(a, b) \subset (- 1, 1)

$(a,b)\subset(-1,1)$ by algebraic polynomials. In the case of half-intervals, the problem is solved completely. We construct an example to illustrate difficulties arising in the case of an open interval.

Keywords: one-sided approximation, characteristic function, polynomials.

Received: 07.09.2015

English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2017, Volume 297, Issue 1, Pages 11–18
DOI: https://doi.org/10.1134/S0081543817050029

Bibliographic databases:

Document Type: Article

UDC: 517.5

Language: Russian

Citation: A. G. Babenko, M. V. Deikalova, S. G. Revesz, “Weighted one-sided approximation of characteristic functions of intervals by polynomials on a closed interval”, Trudy Inst. Mat. i Mekh. UrO RAN, 21, no. 4, 2015, 46–53; Proc. Steklov Inst. Math. (Suppl.), 297, suppl. 1 (2017), 11–18

Citation in format AMSBIB

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\paper Weighted one-sided approximation of characteristic functions of intervals by polynomials on a closed interval

\serial Trudy Inst. Mat. i Mekh. UrO RAN

\yr 2015

\vol 21

\issue 4

\pages 46--53

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\elib{https://elibrary.ru/item.asp?id=25300984}

\transl

\jour Proc. Steklov Inst. Math. (Suppl.)

\yr 2017

\vol 297

\issue , suppl. 1

\pages 11--18

\crossref{https://doi.org/10.1134/S0081543817050029}

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Linking options:

https://www.mathnet.ru/eng/timm1228

https://www.mathnet.ru/eng/timm/v21/i4/p46

This publication is cited in the following 4 articles:

Marina V. Deikalova, Anastasiya Yu. Torgashova, “One-sided $L$ -approximation on a sphere of the characteristic function of a layer”, Ural Math. J., 4:2 (2018), 13–23
M. V. Deikalova, A. Yu. Torgashova, “Nailuchshee odnostoronnee priblizhenie v srednem kharakteristicheskoi funktsii promezhutka algebraicheskimi mnogochlenami”, Tr. IMM UrO RAN, 24, no. 4, 2018, 110–125
M. V. Deikalova, A. Yu. Torgashova, “Best One-Sided Approximation in the Mean of the Characteristic Function of an Interval by Algebraic Polynomials”, Proc. Steklov Inst. Math. (Suppl.), 308:1 (2020), S68–S82
A. Yu. Torgashova, “One-sided integral approximation of the characteristic function of an interval by algebraic polynomials”, Proc. Steklov Inst. Math. (Suppl.), 296, suppl. 1 (2017), 228–235

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Trudy Instituta Matematiki i Mekhaniki UrO RAN

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