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

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},
  MRNUMBER = {MR2356759},
       URL = {http://mfat.imath.kiev.ua/article/?id=428},
}