## Constructive approximation: advanced problems |

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### Contents

Problems of Polynomial Approximation | 1 |

Distribution of Alternation Points of Polynomials of Best Approximation | 4 |

Distribution of Zeros of Polynomials of Best Approximation | 11 |

Copyright | |

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### Common terms and phrases

analytic functions Appendix arbitrary assume Banach space belongs best approximation Blaschke product Borel measure bounded Chapter Chebyshev Chebyshev polynomial compact set compact subset constant contains continuous functions contradiction convergence convex Corollary define definition denote derive disjoint disk dominating set En(f entropy equivalent example exists extreme points finite fixed follows formula function f given Hardy spaces harmonic hence implies inequality integral coefficients interpolation interval knots Kolmogorov l/pn Lebesgue measure Lemma limsup linear logarithmic Lorentz lower estimate measure metric monic polynomial non-negative obtain operator orthogonal orthonormal pn(f Pn(x polynomial of degree positive problem proof of Theorem Proposition prove rational approximation rational function replace Saff satisfies sequence spline subspace Theorem 1.1 theory Tikhomirov trigonometric polynomials uniform norm uniformly unique unit ball vanishes vectors Weierstrass weight widths yields zeros