## Abstract

Let SKn be the maximum of the l_{1} norm, Σ^{n}|x_{k}|, of all nth degree polynomials satisfying |Σ^{n}c_{k}z^{k}| ≦ for |z| =1. We prove that M_{n} is asymptotic to √n, by exhibiting polynomials P_{n} (which are partial sums of certain Fourier series), whose l_{1} norm is asymptotic to √n.

Original language | English (US) |
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Pages (from-to) | 474-481 |

Number of pages | 8 |

Journal | Proceedings of the American Mathematical Society |

Volume | 29 |

Issue number | 3 |

DOIs | |

State | Published - Aug 1971 |

Externally published | Yes |

## Keywords

- Close to constant polynomials
- Coefficients of close to constant modulus
- Extremal polynomials
- Partial sums of fourier series
- U norm of polynomials
- Upper bound for nth derivative

## ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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