Bernstein and markov inequalities for constrained polynomials
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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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