Open Access

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

TitleDirect theorems in the theory of approximation of Banach space vectors by exponential type entire vectors
SourceMethods Funct. Anal. Topology, Vol. 13 (2007), no. 3, 267-278
MathSciNet MR2356759
CopyrightThe 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


Google Scholar Metrics

Citing articles in Google Scholar
Similar articles in Google Scholar

Export article

Save to Mendeley



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},
}


All Issues