Direct Theorems in the Theory of Approximation of the Banach Space Vectors by Entire Vectors of Exponential Type

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For an arbitrary operator A on a Banach space X which is a generator of C_0-group with certain growth condition at the infinity, the direct theorems on connection between the smoothness degree of a vector $x\in X$ with respect to the operator A, the order of convergence to zero of the best approximation of x by exponential type entire vectors for the operator A, and the k-module of continuity are given. Obtained results allows to acquire Jackson-type inequalities in many classic spaces of periodic functions and weighted $L_p$ spaces.
13 pages, typos corrected

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Functional Analysis, Spectral Theory, 41A25; 41A17; 41A65

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http://salesiana.dossiersoluciones.com/handle/123456789/169553

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0704.0298
 http://arxiv.org/abs/0704.0298
 Grushka Ya. and Torba S., "Direct Theorems in the Theory of Approximation of Banach Space Vectors by Exponential Type Entire Vectors", Methods Funct. Anal. Topology. 11 (2007), no. 3, 267-278

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