Improvement Taykov's lower bound in an inequation between C and L norms for trigonometric polynomials
arXiv:math/0212037
Abstract
We give new lower asymptotical estimate of constant \[ C_n=\sup\biggl\{\frac{\|t_n\|_{C(\mathbb T)}}{\|t_n\|_{L(\mathbb T)}}:t_n\text{are real trigonometric polynomials}, \operatorname{deg}t_n<n\biggr\} \] as . This estimate improves known bound of L.V.Taykov (1965).
3 pages