Sharp Markov–Nikol’skii inequality with respect to the uniform norm and the integral norm with Chebyshev weight

• Ivan E. Simonov ^[1] ; Polina Yu. Glazyrina ^[1]
  1. [1] Ural Federal University

     Ural Federal University

     Rusia

     
• Localización: Journal of approximation theory, ISSN 0021-9045, Vol. 192, Nº 1 (April 2015), 2015, págs. 69-81
• Idioma: inglés
• DOI: 10.1016/j.jat.2014.10.009
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• Resumen

  • We study the inequality between the uniform norm of the derivative of an algebraic polynomial of degree nn and the integral norm of this polynomial with Chebyshev weight on a closed interval. We found exact constants and extremal polynomials for derivatives of any order.