Please use this identifier to cite or link to this item: http://hdl.handle.net/10525/2541

 Title: On the approximation by convolution operators in homogeneous Banach spaces on R^d Authors: Draganov, Borislav Keywords: convolution operatorsingular integralrate of convergencedegree of approximationK-functionalhomogeneous Banach space on Rdtempered distributionFourier-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 URI: http://hdl.handle.net/10525/2541 ISSN: 0205-3217 Appears in Collections: Mathematica Balkanica New Series, Vol. 28, 2014, Fasc. 1-2

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