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Tr. Mat. Inst. Steklova, 2001, Volume 232, Pages 45–57 (Mi tm203)  

This article is cited in 9 scientific papers (total in 9 papers)

Polynomials of Least Deviation from Zero and Chebyshev-Type Cubature Formulas

N. N. Andreev, V. A. Yudin


Abstract: The problem about a polynomial of least deviation from zero on a multidimensional sphere is solved in some special cases. For known spherical configurations, a family of subspaces of harmonic polynomials is described for which the Chebyshev-type cubature formulas on the sphere are exact.

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English version:
Proceedings of the Steklov Institute of Mathematics, 2001, 232, 39–51

Bibliographic databases:

Document Type: Article
UDC: 517.5
Received in September 2000

Citation: N. N. Andreev, V. A. Yudin, “Polynomials of Least Deviation from Zero and Chebyshev-Type Cubature Formulas”, Function spaces, harmonic analysis, and differential equations, Collected papers. Dedicated to the 95th anniversary of academician Sergei Mikhailovich Nikol'skii, Tr. Mat. Inst. Steklova, 232, Nauka, MAIK Nauka/Inteperiodika, M., 2001, 45–57; Proc. Steklov Inst. Math., 232 (2001), 39–51

Citation in format AMSBIB
\Bibitem{AndYud01}
\by N.~N.~Andreev, V.~A.~Yudin
\paper Polynomials of Least Deviation from Zero and Chebyshev-Type Cubature Formulas
\inbook Function spaces, harmonic analysis, and differential equations
\bookinfo Collected papers. Dedicated to the 95th anniversary of academician Sergei Mikhailovich Nikol'skii
\serial Tr. Mat. Inst. Steklova
\yr 2001
\vol 232
\pages 45--57
\publ Nauka, MAIK Nauka/Inteperiodika
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm203}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=1851439}
\zmath{https://zbmath.org/?q=an:1001.41016}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2001
\vol 232
\pages 39--51


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

    This publication is cited in the following articles:
    1. Xu Y., “On polynomials of least deviation from zero in several variables”, Experimental Mathematics, 13:1 (2004), 103–112  crossref  mathscinet  zmath  isi  scopus  scopus
    2. V. A. Yudin, “Polynomials of Least Deviation from Zero”, Math. Notes, 78:2 (2005), 279–284  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. Xu Y., “Monomial orthogonal polynomials of several variables”, Journal of Approximation Theory, 133:1 (2005), 1–37  crossref  mathscinet  zmath  isi  scopus
    4. Xu Yu., “Analysis on the unit ball and on the simplex”, Electronic Transactions on Numerical Analysis, 25 (2006), 284–301  mathscinet  zmath  isi
    5. V. A. Yudin, “On Polynomials of Best Approximation”, Math. Notes, 82:4 (2007), 564–568  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    6. Ganzburg M., “Invariance theorems in approximation theory and their applications”, Constructive Approximation, 27:3 (2008), 289–321  crossref  mathscinet  zmath  isi  scopus  scopus
    7. V. A. Yudin, “Invariants and Chebyshev polynomials”, Proc. Steklov Inst. Math. (Suppl.), 265, suppl. 1 (2009), S227–S245  mathnet  crossref  isi  elib
    8. Moale I., Peherstorfer F., “An explicit class of min-max polynomials on the ball and on the sphere”, J Approx Theory, 163:6 (2011), 724–737  crossref  mathscinet  zmath  isi  scopus  scopus
    9. V. A. Yudin, “Polynomials of least deviation from zero”, Proc. Steklov Inst. Math., 280 (2013), 292–295  mathnet  crossref  crossref  mathscinet  isi  elib
  •    . . .  Proceedings of the Steklov Institute of Mathematics
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