Author(s): I.P. Natanson.
Publisher: Frederick Ungar
Year: 1964
Language: English
Pages: 240
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
