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

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:
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, Trudy 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 Trudy 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
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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
2. V. A. Yudin, “Polynomials of Least Deviation from Zero”, Math. Notes, 78:2 (2005), 279–284
3. Xu Y., “Monomial orthogonal polynomials of several variables”, Journal of Approximation Theory, 133:1 (2005), 1–37
4. Xu Yu., “Analysis on the unit ball and on the simplex”, Electronic Transactions on Numerical Analysis, 25 (2006), 284–301
5. V. A. Yudin, “On Polynomials of Best Approximation”, Math. Notes, 82:4 (2007), 564–568
6. Ganzburg M., “Invariance theorems in approximation theory and their applications”, Constructive Approximation, 27:3 (2008), 289–321
7. V. A. Yudin, “Invariants and Chebyshev polynomials”, Proc. Steklov Inst. Math. (Suppl.), 265, suppl. 1 (2009), S227–S245
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
9. V. A. Yudin, “Polynomials of least deviation from zero”, Proc. Steklov Inst. Math., 280 (2013), 292–295
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