Theory of Uniform Approximation of Functions by PolynomialsWalter De Gruyter, 2008 - 480페이지 Review text: "The book could be of interest for all who work in approximation theory and related fields; it should not be overlooked by university libraries."In: Ems Newsletter 3/2009 "It is useful for students interested in uniform approximation theory, and it can be used as a reference book for researchers as well."In: L'Enseignement Mathématique 2/2008. |
목차
Chebyshev theory and its development | 1 |
Weierstrass theorems | 111 |
On smoothness of functions | 167 |
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2-snakes a₁ Akad algebraic polynomial approximation of functions arbitrary arccos assume b₁ Bernstein best approximation best uniform approximation Chebyshev polynomials Chebyshev system classes coefficients complex const continuous functions Corollary defined Definition denote derivative differentiable Dirichlet kernels divided difference Dokl Dzyadyk En(f equality estimate Fejér kernel following inequality following properties Fourier series hence Hölder Hölder classes integral interpolation kernels Kiev Lagrange polynomial Lemma Let us prove linear Math modulus of continuity Nauk SSSR necessary and sufficient nomial obtain P₁ periodic functions points x₁ polynomial of degree polynomial Pn possesses the following problem Russian segment Shevchuk space Stechkin system of functions t₁ Theorem 1.2 theory of approximation tion trigonometric polynomial Vallée Poussin variables virtue w₁(t WH[k yields zeros π π Φη