Israel Journal of Mathematics

, Volume 76, Issue 1, pp 183–192

Notes on lacunary Müntz polynomials

  • Peter Borwein
  • Tamás Erdélyi

DOI: 10.1007/BF02782851

Cite this article as:
Borwein, P. & Erdélyi, T. Israel J. Math. (1991) 76: 183. doi:10.1007/BF02782851


We prove that a Müntz system has Chebyshev polynomials on [0,1] with uniformly bounded coefficients if and only if it is lacunary. A sharp Bernstein-type inequality for lacunary Müntz systems is established as well. As an application we show that a lacunary Müntz system fails to be dense inC(A) in the uniform norm for everyA ⊂ [0,1] with positive outer Lebesgue measure. A bounded Remez-type inequality is conjectured for non-dense Müntz systems on [0,1] which would solve Newman’s problem concerning the density of products of Müntz systems.

Copyright information

© Hebrew University 1991

Authors and Affiliations

  • Peter Borwein
    • 1
  • Tamás Erdélyi
    • 2
  1. 1.Department of MathematicsDalhousie UniversityHalifaxCanada
  2. 2.Department of MathematicsThe Ohio State UniversityColumbusUSA

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