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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika
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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2010, Number 10, Pages 60–68 (Mi ivm7140)  
This article is cited in 4 scientific papers (total in 4 papers)

The Lagrange trigonometric interpolation polynomial with the minimal norm considered as an operator from $C_{2\pi}$ to $C_{2\pi}$

I. A. Shakirov

Chair of Mathematical Analysis, Naberezhnye Chelny State Pedagogical Institute, Naberezhnye Chelny, Russia
Full-text PDF (178 kB) Citations (4)
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Abstract: In this paper we perform a comparative analysis of Lebesgue functions and constants of a family of Lagrange polynomials. We prove that if a polynomial from the family has the minimal norm in the space of square summable functions, then it also has the minimal norm as an operator which maps a space of continuous functions into itself.
Keywords: Lagrange polynomials, fundamental polynomials, Lebesgue functions, Lebesgue constants.
Received: 09.02.2009
Revised: 19.06.2009
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2010, Volume 54, Issue 10, Pages 52–59
DOI: https://doi.org/10.3103/S1066369X10100063
Bibliographic databases:
Document Type: Article
UDC: 517.518
Language: Russian
Citation: I. A. Shakirov, “The Lagrange trigonometric interpolation polynomial with the minimal norm considered as an operator from $C_{2\pi}$ to $C_{2\pi}$”, Izv. Vyssh. Uchebn. Zaved. Mat., 2010, no. 10, 60–68; Russian Math. (Iz. VUZ), 54:10 (2010), 52–59
Citation in format AMSBIB
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\by I.~A.~Shakirov
\paper The Lagrange trigonometric interpolation polynomial with the minimal norm considered as an operator from $C_{2\pi}$ to~$C_{2\pi}$
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2010
\issue 10
\pages 60--68
\mathnet{http://mi.mathnet.ru/ivm7140}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2808742}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2010
\vol 54
\issue 10
\pages 52--59
\crossref{https://doi.org/10.3103/S1066369X10100063}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-78649618261}
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  • https://www.mathnet.ru/eng/ivm/y2010/i10/p60
    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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    References:90
    First page:19
     
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