Theory of Uniform Approximation of Functions by PolynomialsWalter de Gruyter, 2008. 9. 25. - 495페이지 A thorough, self-contained and easily accessible treatment of the theory on the polynomial best approximation of functions with respect to maximum norms. The topics include Chebychev theory, Weierstraß theorems, smoothness of functions, and continuation of functions. |
목차
| 1 | |
Chapter 2 Weierstrass theorems | 111 |
Chapter 3 On smoothness of functions | 167 |
Chapter 4 Extension | 299 |
Chapter 5 Direct theorems on the approximation of periodic functions | 331 |
Chapter 6 Inverse theorems on the approximation of periodic functions | 345 |
Chapter 7 Approximation by polynomials | 379 |
| 437 | |
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2-snakes Akad algebraic polynomial approximation of functions arbitrary arccos assume Bernstein best approximation best uniform approximation Chebyshev polynomials Chebyshev system classes condition const continuous functions Corollary defined Definition denote derivative Dirichlet kernels divided difference Dokl Dzyadyk En(f equality estimate Fejér kernel following inequality following properties Fourier series function f g₁(x hence Hölder classes integral interpolation kernels Kiev Lagrange polynomial Lemma Let us prove linear Math modulus of continuity Nauk SSSR nomial obtain periodic functions point x0 polynomial of degree polynomial Pn possesses the following problem Russian satisfies Shevchuk space Stechkin system of functions t₁ Theorem 1.2 theory of approximation tion Tn(t trigonometric polynomial Vallée Poussin variables virtue WH[k x₁ yields zeros π π Φη Φο