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Bernstein and markov inequalities for constrained polynomials

  • Michael A. Lachance
Approximation And Interpolation Theory
Part of the Lecture Notes in Mathematics book series (LNM, volume 1105)

Abstract

Pointwise and uniform bounds are determined for the derivatives of real algebraic polynomials p(x) which on the interval [−1,1] satisfy (1−x2)λ/2|p(x)| ≤ 1, λ a fixed positive integer. The pointwise bounds are investigated with regard to their sharpness while the uniform bounds are shown to be best possible in an asymptotic sense.

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Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Michael A. Lachance
    • 1
  1. 1.Department of MathematicsUniversity of Michigan-DearbornDearbornUSA

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