## Strong Asymptotics for Extremal Polynomials Associated with Weights on R0. The results are consequences of a strengthened form of the following assertion: Given 0 p |

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### Contents

Introduction | 1 |

Notation and Index of Notation | 12 |

Weighted Polynomials and Zeros of Extremal Polynomials | 24 |

Copyright | |

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Approximation Theory asymptotic upper bound Cauchy-Schwarz inequality choose closed subsets compact subsets conformal map continuous in 1.1 Corollary 8.2 denote dp(x E.B. Saff Edited entire function exists extremal polynomials follows Freud Further G[W(anx H.N. Mhaskar Hence IIP Wll IIPWII independent integer integral Jackson's theorem Lagrange interpolation largest zero leading coefficient Lemma Let W(x lim llg(x lim sup lira log n)/n log|x-t lower bound Maclaurin series Mhaskar and Saff monic monic polynomial Nevai non-negative function notation Note nth root obtain orthogonal polynomials orthonormal polynomial polynomial approximations polynomial of degree positive in 1.1 positive integer positive number Proceedings Proof of Theorem recurrence relation coefficients right-hand side Saff 46 sequence shows strong asymptotics subsets of C\[-l.1 Theorem 3.1 Theory Totik v n n weighted polynomial x)W(a x yields zero distribution