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Title: On the approximation by convolution operators in homogeneous Banach spaces on R^d
Authors: Draganov, Borislav
Keywords: convolution operator
singular integral
rate of convergence
degree of approximation
homogeneous Banach space on Rd
tempered distribution
Fourier-Stieltjes transform
Issue Date: 2014
Publisher: Bulgarian Academy of Sciences - National Committee for Mathematics
Citation: Mathematica Balkanica New Series, Vol. 28, Fasc 1-2 (2014), 3p-30p
Abstract: The 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.
Description: AMS Subject Classification 2010: 41A25, 41A35, 41A40, 41A63, 41A65, 42A38, 42A85, 42B10, 42B20
ISSN: 0205-3217
Appears in Collections:Mathematica Balkanica New Series, Vol. 28, 2014, Fasc. 1-2

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