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

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

2007-04-03

arxiv.org/abs/0704.0298v3

Grushka Ya. and Torba S., "Direct Theorems in the Theory of Approximation of Banach Space Vectors by Exponential Type Entire V

Mathematics

Functional Analysis

13 pages, typos corrected

Scientific paper

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.

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