## Abstract

Let E_{l} = ∪_{j=1}^{l} [a_{2j-i} , a_{2j}], a_{1} < a_{2} < ... < a_{2l}. First we give a complete characterization of that polynomial of degree n which has n + l extremal points on E_{l}. Such a polynomial is called T-polynomial because it shares many properties with the classical Chebyshev polynomial on [-1, 1], e.g., it is minimal with respect to the maximum norm on E_{l}, its derivative is minimal with respect to the L_{1}-norm on E_{l}, etc. It is known that T-polynomials do not exist on every E_{l}. Then it is demonstrated how to generate in a very simple illustrative geometric way from a T-polynomial on l intervals a T-polynomial on l or more intervals. For the case of two and three intervals a complete description of those intervals on which there exists a T-polynomial is provided. Finally, we show how to compute T-polynomials by Newton's method.

Original language | English |
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Pages (from-to) | 27-58 |

Number of pages | 32 |

Journal | Acta Mathematica Hungarica |

Volume | 83 |

Issue number | 1-2 |

Publication status | Published - Apr 1999 |

Externally published | Yes |