On the approximation by convolution operators in homogeneous Banach spaces on R^d

Draganov, Borislav. "On the approximation by convolution operators in homogeneous Banach spaces on R^d." Mathematica Balkanica New Series 28.1-2 (2014): 3-30. <http://eudml.org/doc/281420>.

@article{Draganov2014,
abstract = {AMS Subject Classification 2010: 41A25, 41A35, 41A40, 41A63, 41A65, 42A38, 42A85, 42B10, 42B20The paper presents a description of the optimal rate of approximation as well as of a broad class of functions that possess it for convolution operators acting in the so-called homogeneous Banach spaces of functions on Rd. The description is the same in any such space and uses the Fourier transform. Simple criteria for establishing upper estimates of the approximation error via a K-functional are given. The differential operator in the K-functional is defined similarly to the infinitesimal generator by means of the convolution operator.},
author = {Draganov, Borislav},
journal = {Mathematica Balkanica New Series},
keywords = {convolution operator; singular integral; rate of convergence; degree of approximation; K-functional; homogeneous Banach space on Rd; tempered distribution; Fourier-Stieltjes transform},
language = {eng},
number = {1-2},
pages = {3-30},
publisher = {Bulgarian Academy of Sciences - National Committee for Mathematics},
title = {On the approximation by convolution operators in homogeneous Banach spaces on R^d},
url = {http://eudml.org/doc/281420},
volume = {28},
year = {2014},
}

TY - JOUR
AU - Draganov, Borislav
TI - On the approximation by convolution operators in homogeneous Banach spaces on R^d
JO - Mathematica Balkanica New Series
PY - 2014
PB - Bulgarian Academy of Sciences - National Committee for Mathematics
VL - 28
IS - 1-2
SP - 3
EP - 30
AB - AMS Subject Classification 2010: 41A25, 41A35, 41A40, 41A63, 41A65, 42A38, 42A85, 42B10, 42B20The paper presents a description of the optimal rate of approximation as well as of a broad class of functions that possess it for convolution operators acting in the so-called homogeneous Banach spaces of functions on Rd. The description is the same in any such space and uses the Fourier transform. Simple criteria for establishing upper estimates of the approximation error via a K-functional are given. The differential operator in the K-functional is defined similarly to the infinitesimal generator by means of the convolution operator.
LA - eng
KW - convolution operator; singular integral; rate of convergence; degree of approximation; K-functional; homogeneous Banach space on Rd; tempered distribution; Fourier-Stieltjes transform
UR - http://eudml.org/doc/281420
ER -