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- W2083001521 abstract "Generalizing a number of earlier results, P. Borwein established a sharp Markov-type inequality on $[ - 1,1]$ for the derivatives of polynomials $p in {pi _n}$ having at most $k(0 leq k leq n)$ zeros in the complex unit disk. Using Lorentz representation and a Markov-type inequality for the derivative of Müntz polynomials due to D. Newman, we give a surprisingly short proof of Borweinâs Theorem. The new result of this paper is to obtain a sharp Bernstein-type analogue of Borweinâs Theorem. By the same method we prove a sharp Bernstein-type inequality for another wide family of classes of constrained polynomials." @default.
- W2083001521 created "2016-06-24" @default.
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- W2083001521 date "1991-03-01" @default.
- W2083001521 modified "2023-10-18" @default.
- W2083001521 title "Bernstein-type inequalities for the derivatives of constrained polynomials" @default.
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- W2083001521 doi "https://doi.org/10.1090/s0002-9939-1991-1036985-7" @default.
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