English

Improvement Taykov's lower bound in an inequation between C and L norms for trigonometric polynomials

Classical Analysis and ODEs 2007-05-23 v1 Number Theory

Abstract

We give new lower asymptotical estimate of constant Cn=sup{tnC(T)tnL(T):tnare real trigonometric polynomials,degtn<n} 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 nn\to\infty. This estimate improves known bound of L.V.Taykov (1965).

Keywords

Cite

@article{arxiv.math/0212037,
  title  = {Improvement Taykov's lower bound in an inequation between C and L norms for trigonometric polynomials},
  author = {D. V. Gorbachev},
  journal= {arXiv preprint arXiv:math/0212037},
  year   = {2007}
}

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3 pages