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On the unicity in simultaneous approximation by algebraic polynomials

โœ Scribed by E Kimchi; N Richter-Dyn


Publisher
Elsevier Science
Year
1976
Tongue
English
Weight
94 KB
Volume
18
Category
Article
ISSN
0021-9045

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A Characterization of Smoothness in Term
โœ V.A. Operstein ๐Ÿ“‚ Article ๐Ÿ“… 1995 ๐Ÿ› Elsevier Science ๐ŸŒ English โš– 307 KB

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