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

Mathematica Balkanica New Series (2014)

- Volume: 28, Issue: 1-2, page 3-30
- ISSN: 0205-3217

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topDraganov, 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 -

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