Constructive Approximation - George G. Lorentz

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Résumé :
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Sommaire:
1. Problems of Polynomial Approximation.- ? 1. Examples of Polynomials of Best Approximation.- ? 2. Distribution of Alternation Points of Polynomials of Best Approximation.- ? 3. Distribution of Zeros of Polynomials of Best Approximation.- ? 4. Error of Approximation.- ? 5. Approximation on (-?, ?) by Linear Combinations of Functions (x - c)-1.- ? 6. Weighted Approximation by Polynomials on (-?, ?).- ? 7. Spaces of Approximation Theory.- ? 8. Problems and Notes.- 2. Approximation Problems with Constraints.- ?1. Introduction.- ? 2. Growth Restrictions for the Coefficients.- ? 3. Monotone Approximation.- ? 4. Polynomials with Integral Coefficients.- ? 5. Determination of the Characteristic Sets.- ? 6. Markov-Type Inequalities.- ? 7. The Inequality of Remez.- ? 8. One-sided Approximation by Polynomials.- ?9. Problems.- ? 10. Notes.- 3. Incomplete Polynomials.- ? 1. Incomplete Polynomials.- ? 2. Incomplete Chebyshev Polynomials.- ? 3. Incomplete Trigonometric Polynomials.- ? 4. Sequences of Polynomials with Many Real Zeros.- ?5. Problems.- ?6. Notes.- 4. Weighted Polynomials.- ? 1. Essential Sets of Weighted Polynomials.- ? 2. Weighted Chebyshev Polynomials.- ?3. The Equilibrium Measure.- ? 4. Determination of Minimal Essential Sets.- ? 5. Weierstrass Theorems and Oscillations.- ? 6. Weierstrass Theorem for Freud Weights.- ?7. Problems.- ?8. Notes.- 5. Wavelets and Orthogonal Expansions.- ? 1. Multiresolutions and Wavelets.- ? 2. Scaling Functions with a Monotone Majorant.- ? 3. Periodization.- ? 4. Polynomial Schauder Bases.- ? 5. Orthonormal Polynomial Bases.- ? 6. Problems and Notes.- 6. Splines.- ?1. General Facts.- ? 2. Splines of Best Approximation.- ? 3. Periodic Splines.- ? 4. Convergence of Some Spline Operators.-?5. Notes.- 7. Rational Approximation.- ?1. Introduction.- ?2. Best Rational Approximation.- ? 3. Rational Approximation of