### Abstract

For an arbitrary operator $A$ on a Banach space $X$ which is the generator of a $C_0$-group with certain growth condition at infinity, direct theorems on connection between the degree of smoothness of a vector $x\in X$ with respect to the operator $A$, the rate 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 established. The results allow to obtain Jackson-type inequalities in a number of classic spaces of periodic functions and weighted $L_p$ spaces.

### Full Text

### Article Information

Title | Direct theorems in the theory of approximation of Banach space vectors by exponential type entire vectors |

Source | Methods Funct. Anal. Topology, Vol. 13 (2007), no. 3, 267-278 |

MathSciNet |
MR2356759 |

Copyright | The Author(s) 2007 (CC BY-SA) |

### Authors Information

*Ya. Grushka*

Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Teresh\-chenkivs'ka, Kyiv, 01601, Ukraine

* S. Torba*

Institute of Mathematics, National Academy of Sciences of Ukraine, 3 Teresh\-chenkivs'ka, Kyiv, 01601, Ukraine

### Citation Example

Ya. Grushka and S. Torba, *Direct theorems in the theory of approximation of Banach space vectors by exponential type entire vectors*, Methods Funct. Anal. Topology **13**
(2007), no. 3, 267-278.

### BibTex

@article {MFAT428,
AUTHOR = {Grushka, Ya. and Torba, S.},
TITLE = {Direct theorems in the theory of approximation of Banach space vectors by exponential type entire vectors},
JOURNAL = {Methods Funct. Anal. Topology},
FJOURNAL = {Methods of Functional Analysis and Topology},
VOLUME = {13},
YEAR = {2007},
NUMBER = {3},
PAGES = {267-278},
ISSN = {1029-3531},
URL = {http://mfat.imath.kiev.ua/article/?id=428},
}

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