CONSTRUCTIVE FUNCTION THEORY VOL. I: UNIFORM APPROXIMATION. Vol.1

Contents......Page all_12023_to_00240.cpc0003.djvu Introduction......Page all_12023_to_00240.cpc0005.djvu 1. Weierstrass' First Theorem......Page all_12023_to_00240.cpc0011.djvu 2. Weierstrass' Second Approximation Theorem......Page all_12023_to_00240.cpc0017.djvu 3. The Reciprocal Coherence between the Two Weierstrass Theorems......Page all_12023_to_00240.cpc0024.djvu 1. Fundamental Concepts......Page all_12023_to_00240.cpc0028.djvu 2. Tchebysheff's Theorems......Page all_12023_to_00240.cpc0035.djvu 3. Examples. The Tchebysheff Polynomials......Page all_12023_to_00240.cpc0042.djvu 4. Other Properties of Tchebysheff Polynomials......Page all_12023_to_00240.cpc0050.djvu 1. The Roots of a Trigonometric Polynomial......Page all_12023_to_00240.cpc0065.djvu 2. The Image Point Method......Page all_12023_to_00240.cpc0067.djvu 3. The Trigonometric Polynomial of the Best Approximation......Page all_12023_to_00240.cpc0072.djvu 4. P. L. Tchebysheff's Theorems......Page all_12023_to_00240.cpc0073.djvu 5. Examples......Page all_12023_to_00240.cpc0080.djvu 1. Formulation of Problem. Modulus of Continuity; A Lipschitz Condition......Page all_12023_to_00240.cpc0083.djvu 2. Lemmata......Page all_12023_to_00240.cpc0087.djvu 3. D. Jackson's Theorems......Page all_12023_to_00240.cpc0092.djvu 1. S. N. Bernstein's Inequality......Page all_12023_to_00240.cpc0098.djvu 2. Some Elements of Theory of Series......Page all_12023_to_00240.cpc0101.djvu 3. S. N. Bernstein's Theorems......Page all_12023_to_00240.cpc0105.djvu 4. A. Zygmund's Theorems......Page all_12023_to_00240.cpc0114.djvu 5. The Existence of Functions with Preassigned Best Approximation......Page all_12023_to_00240.cpc0117.djvu 6. Density of Class H% in Class LipM a......Page all_12023_to_00240.cpc0126.djvu 1. Lemmata......Page all_12023_to_00240.cpc0128.djvu 2. How the Structural Properties of a Function Affect Its Approximation......Page all_12023_to_00240.cpc0133.djvu 3. Converse Theorems......Page all_12023_to_00240.cpc0137.djvu 4. Bernstein's Second Inequality......Page all_12023_to_00240.cpc0141.djvu 5. Existence of a Function with Preassigned Approximations......Page all_12023_to_00240.cpc0144.djvu 6. The Markoff Inequality......Page all_12023_to_00240.cpc0145.djvu 1. The Fourier Series......Page all_12023_to_00240.cpc0150.djvu 2. Estimate of the Deviation of Partial Sums of a Fourier Series......Page all_12023_to_00240.cpc0157.djvu 3. Example of a Continuous Function Not Expandable in a Fourier Series......Page all_12023_to_00240.cpc0161.djvu 1. Fejér Sums......Page all_12023_to_00240.cpc0165.djvu 2. Some Estimates of Fejér Sums......Page all_12023_to_00240.cpc0169.djvu 3. De la Vallée-Poussin's Sums......Page all_12023_to_00240.cpc0175.djvu 1. The Concept of Analytic Functions......Page all_12023_to_00240.cpc0180.djvu 2. S. N. Bernstein's Theorems on the Best Approximation to Periodic Analytic Functions......Page all_12023_to_00240.cpc0185.djvu 3. The Best Approximation to Functions Analytic on a Segment......Page all_12023_to_00240.cpc0191.djvu 1. Expansion by Tchebysheff Polynomials......Page all_12023_to_00240.cpc0203.djvu 2. Some Properties of Bernstein's Polynomials......Page all_12023_to_00240.cpc0204.djvu 3. Some Properties of de la Vallée-Poussin's Integral......Page all_12023_to_00240.cpc0214.djvu 4. Bernstein-Rogosinsky's Sums......Page all_12023_to_00240.cpc0225.djvu 5. Convergence Factors......Page all_12023_to_00240.cpc0228.djvu Bibliography......Page all_12023_to_00240.cpc0235.djvu Index......Page all_12023_to_00240.cpc0239.djvu Index of Symbols......Page all_12023_to_00240.cpc0240.djvu