## Abstract

For p»2, letmp, n be the minimum of the L^{p} norm all nth degree polynomials Σ^{n}ake^{ikt} ateikt which satisfy |ak| =1, k = 0, 1, ···, n. We exhibit certain polynomials Pn whose L^{p} norm(2<p<∞) is asymptotic to √n, thereby proving that mp, n is itself asymptotic to √n. We also show that the sup norm of (essentially) the same polynomials isasymptotic to (1.1716 …)X√n.

Original language | English |
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Pages (from-to) | 249-259 |

Number of pages | 11 |

Journal | Proceedings of the American Mathematical Society |

Volume | 30 |

Issue number | 2 |

DOIs | |

State | Published - Oct 1971 |

Externally published | Yes |

## Keywords

- Close to constant polynomials
- Coefficients of constant modulus
- Extremal polynomials
- Fresnel integral
- L norms of polynomials
- Sup norm of polynomials
- Van der corput's lemma

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