Title | AN INEQUALITY OF DUFFIN-SCHAEFFER-SCHUR TYPE |
Publication Type | Journal Article |
Year of Publication | 1998 |
Authors | Nikolov G |
Journal | Annuaire de l’Université de Sofia “St. Kliment Ohridski”. Faculté de Mathématiques et Informatique |
Volume | 90 |
Issue | Livre 1 - Mathématiques et Mecanique |
Pagination | 109-123 |
ISSN | 0205-0808 |
Keywords | Chebyshev polynomials, Markov inequality |
Abstract | 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 $\bigg\{ \cos \frac{j\pi}{n} \big/ \cos \frac{\pi}{n+1}\bigg\}_{j=1}^{n-1}$. |
1991/95 MSC | 41A17, 26D05 |
Attachment | Size |
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90-109-123.pdf | 1.12 MB |