Markov- and Bernstein-type Inequalities for Polynomials with Restricted Coefficients
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چکیده
The Markov-type inequality ‖p′‖[0,1] ≤ cn log(n + 1)‖p‖[0,1] is proved for all polynomials of degree at most n with coefficients from {−1, 0, 1} with an absolute constant c. Here ‖·‖[0,1] denotes the supremum norm on [0, 1]. The Bernstein-type inequality |p′(y)| ≤ c (1 − y)2 ‖p‖[0,1] , y ∈ [0, 1) , is shown for every polynomial p of the form
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تاریخ انتشار 1999