# On the Approximation by Convolution Operators in Homogeneous Banach Spaces of Periodic Functions

Mathematica Balkanica New Series (2011)

- Volume: 25, Issue: 1-2, page 39-59
- ISSN: 0205-3217

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topDraganov, Borislav R.. "On the Approximation by Convolution Operators in Homogeneous Banach Spaces of Periodic Functions." Mathematica Balkanica New Series 25.1-2 (2011): 39-59. <http://eudml.org/doc/281493>.

@article{Draganov2011,

abstract = {AMS Subject Classification 2010: 41A25, 41A27, 41A35, 41A36, 41A40, 42Al6, 42A85.The paper is concerned with establishing direct estimates for convolution operators on homogeneous Banach spaces of periodic functions by means of appropriately defined Kfunctional. The differential operator in the K-functional is defined by means of strong limit and described explicitly in terms of its Fourier coefficients. The description is simple and independent of the homogeneous Banach space. Saturation of such operators is also considered.},

author = {Draganov, Borislav R.},

journal = {Mathematica Balkanica New Series},

keywords = {Convolution operator; singular integral; rate of convergence; degree of approximation; K-functional; homogeneous Banach space of periodic functions; Fourier transform; convolution operator; -functional},

language = {eng},

number = {1-2},

pages = {39-59},

publisher = {Bulgarian Academy of Sciences - National Committee for Mathematics},

title = {On the Approximation by Convolution Operators in Homogeneous Banach Spaces of Periodic Functions},

url = {http://eudml.org/doc/281493},

volume = {25},

year = {2011},

}

TY - JOUR

AU - Draganov, Borislav R.

TI - On the Approximation by Convolution Operators in Homogeneous Banach Spaces of Periodic Functions

JO - Mathematica Balkanica New Series

PY - 2011

PB - Bulgarian Academy of Sciences - National Committee for Mathematics

VL - 25

IS - 1-2

SP - 39

EP - 59

AB - AMS Subject Classification 2010: 41A25, 41A27, 41A35, 41A36, 41A40, 42Al6, 42A85.The paper is concerned with establishing direct estimates for convolution operators on homogeneous Banach spaces of periodic functions by means of appropriately defined Kfunctional. The differential operator in the K-functional is defined by means of strong limit and described explicitly in terms of its Fourier coefficients. The description is simple and independent of the homogeneous Banach space. Saturation of such operators is also considered.

LA - eng

KW - Convolution operator; singular integral; rate of convergence; degree of approximation; K-functional; homogeneous Banach space of periodic functions; Fourier transform; convolution operator; -functional

UR - http://eudml.org/doc/281493

ER -

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