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An Extremal Relation of the Theory of Approximation of Functions by Algebraic Polynomials

โœ Scribed by Semyon Rafalson


Publisher
Elsevier Science
Year
2001
Tongue
English
Weight
178 KB
Volume
110
Category
Article
ISSN
0021-9045

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We prove direct and inverse theorems for the classical modulus of smoothness and approximation by algebraic polynomials in \(L_{p}[-1,1]\). These theorems contain the well-known theorems of A. Timan, V. Dzyadyk, G. Freud, and Yu. Brudnyi as special cases when \(p=x\). They also provide a characteriz