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Izv. RAN. Ser. Mat., 2005, Volume 69, Issue 3, Pages 179–192 (Mi izv643)  

This article is cited in 11 scientific papers (total in 11 papers)

Bounds for the derivatives of polynomials on centrally symmetric convex bodies

V. I. Skalyga


Abstract: Exact multidimensional analogues of V. A. Markov's inequality are found for the derivatives of polynomials on centrally symmetric bodies.

DOI: https://doi.org/10.4213/im643

Full text: PDF file (962 kB)
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English version:
Izvestiya: Mathematics, 2005, 69:3, 607–621

Bibliographic databases:

UDC: 517.16
MSC: 26D05, 41A17, 41A63, 46B28, 46G05, 46G20, 46G25, 46M99, 46T20, 52A40, 65D18
Received: 30.09.2003

Citation: V. I. Skalyga, “Bounds for the derivatives of polynomials on centrally symmetric convex bodies”, Izv. RAN. Ser. Mat., 69:3 (2005), 179–192; Izv. Math., 69:3 (2005), 607–621

Citation in format AMSBIB
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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. V. I. Skalyga, “Sharpness conditions in multidimensional analogs of V.  A. Markov's inequality”, Math. Notes, 80:6 (2006), 893–897  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib
    2. V. I. Skalyga, “V. A. Markov's theorems in normed spaces”, Izv. Math., 72:2 (2008), 383–412  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. V. I. Skalyga, “Analogue of A. A. Markov's inequality for polynomials in two variables”, Sb. Math., 199:9 (2008), 1409–1420  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    4. Harris L.A., “Multivariate Markov polynomial inequalities and Chebyshev nodes”, J. Math. Anal. Appl., 338:1 (2008), 350–357  crossref  mathscinet  zmath  isi  elib  scopus
    5. Muñoz-Fernández G.A., Révész S.Gy., Seoane-Sepúlveda J.B., “Geometry of homogeneous polynomials on non symmetric convex bodies”, Math. Scand., 105:1 (2009), 147–160  crossref  mathscinet  zmath  isi
    6. Harris L.A., “A proof of Markov's theorem for polynomials on Banach spaces”, J. Math. Anal. Appl., 368:1 (2010), 374–381  crossref  mathscinet  zmath  isi  scopus
    7. Lawrence A. Harris, “A bivariate Markov inequality for Chebyshev polynomials of the second kind”, Journal of Approximation Theory, 2011  crossref  mathscinet  isi  scopus
    8. Munoz-Fernandez G.A., Sanchez V.M., Seoane-Sepulveda J.B., “L-P-Analogues of Bernstein and Markov Inequalities”, Mathematical Inequalities & Applications, 14:1 (2011), 135–145  crossref  mathscinet  zmath  isi  scopus
    9. Gamez-Merino J.L., Munoz-Fernandez G.A., Sanchez V.M., Seoane-Sepulveda J.B., “Inequalities for Polynomials on the Unit Square via the Krein-Milman Theorem”, J. Convex Anal., 20:1 (2013), 125–142  mathscinet  zmath  isi
    10. Jimenez-Rodriguez P., Munoz-Fernandez G.A., Pellegrino D., Seoane-Sepulveda J.B., “Bernstein-Markov type inequalities and other interesting estimates for polynomials on circle sectors”, Math. Inequal. Appl., 20:1 (2017), 285–300  crossref  mathscinet  isi  scopus
    11. Goldman G., “A Case of Multivariate Birkhoff Interpolation Using High Order Derivatives”, J. Approx. Theory, 223 (2017), 19–28  crossref  mathscinet  zmath  isi  scopus
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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