AN INEQUALITY OF DUFFIN-SCHAEFFER-SCHUR TYPE
Keywords:
Chebyshev polynomials, Markov inequalityAbstract
It is shown here that the transformed Chebyshev polynomial of the second kind $\overline{U}_{n}(x) := U_{n}\big (x \cos \frac{\pi}{n+1} \big )$ has the greatest uniform norm in [-1, 1] of its $k$-th derivative ($k = 1,...,n$) among all algebraic polynomials of degree not exceeding $n$, which vanish at $\pm 1$ and whose absolute value is less than or equal to 1 at the points $\bigg\{ \cos \frac{j\pi}{n} \big/ \cos \frac{\pi}{n+1}\bigg\}_{j=1}^{n-1}$.
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Published
1998-12-12
How to Cite
Nikolov, G. (1998). AN INEQUALITY OF DUFFIN-SCHAEFFER-SCHUR TYPE. Ann. Sofia Univ. Fac. Math. And Inf., 90, 109–123. Retrieved from https://ftl5.uni-sofia.bg/index.php/fmi/article/view/289
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