Multivariate Markov polynomial inequalities and Chebyshev nodes

Lawrence A. Harris

Research output: Contribution to journalArticlepeer-review

12 Scopus citations


This article considers the extension of V.A. Markov's theorem for polynomial derivatives to polynomials with unit bound on the closed unit ball of any real normed linear space. We show that this extension is equivalent to an inequality for certain directional derivatives of polynomials in two variables that have unit bound on the Chebyshev nodes. We obtain a sharpening of the Markov inequality for polynomials whose values at specific points have absolute value less than one. We also obtain an interpolation formula for polynomials in two variables where the interpolation points are Chebyshev nodes.

Original languageEnglish
Pages (from-to)350-357
Number of pages8
JournalJournal of Mathematical Analysis and Applications
Issue number1
StatePublished - Feb 1 2008


  • Bivariate Lagrange polynomials
  • Bivariate polynomial interpolation
  • Chebyshev nodes
  • Markov's theorem
  • Normed linear spaces
  • Polynomial operators

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics


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