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1 (p1): Chapter I.PRELIMINARIES 1 (p1-1): 1.Statement of the Problems;Notation 8 (p1-2): 2.Lipschitz Conditions and Derivatives 30 (p1-3): 3.Exercises 31 (p1-4): 4.Discussion 33 (p2): PART I.PROBLEM α 33 (p2-1): Chapter II.POLYNOMIAL INEQUALITIES 33 (p2-1-1): 1.A Polynomial and its Derivarives 40 (p2-1-2): 2.A Polynomial and its Integral 43 (p2-1-3): 3.The Lagrange-Hermite Interpolation Formula 44 (p2-1-4): 4.Geometric Properties of Equipotential Curves 48 (p2-1-5): 5.Equally Distributed Points 75 (p2-1-6): 6.Exercises 78 (p2-1-7): 7.Open Problems 81 (p2-2): Chapter III.TCHEBYCHEFF APPROXIMATION 81 (p2-2-1): 1.Jackson's Theorem on Trigonometric Approximation 90 (p2-2-2): 2.Direct Theorems 96 (p2-2-3): 3.The Faber Polynomials 100 (p2-2-4): 4.Indirect Theorems 108 (p2-2-5): 5.The Derivative and Integral of a Function 111 (p2-2-6): 6.Best Approximation 112 (p2-2-7): 7.Exercises 114 (p2-2-8): 8.Open Problems 117 (p2-3): Chapter IV.APPROXIMATION MEASURED BY A LINE INTEGRAL 117 (p2-3-1): 1.Direct Theorems 120 (p2-3-2): 2.Indirect Theorems 126 (p2-3-3): 3.Orthogonal Polynomials 131 (p2-3-4): 4.Polynomials of Best Approximation 133 (p2-3-5): 5.Generality of the Weight Function 135 (p2-3-6)

Author

W.E.Sewell

Published

1942

Language

EN