On convergence of families of linear polynomial operators
Vladimir I. Rukasov, Konstantin V. Runovski, and Hans-Jürgen Schmeisser
Source: Funct. Approx. Comment. Math. Volume 41, Number 1
(2009), 41-54.
Abstract
The convergence of families of linear polynomial operators in the scale of the $L_p$-spaces with $0<p<+\infty$ is studied. The convergence conditions are formulated in terms of the Fourier transform of the generator of the kernel. The results are applied to methods generated by classical kernels.
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Keywords: approximation; trigonometric polynomials; Lp-convergence; classical means; Fourier transform
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Links and Identifiers
Permanent link to this document: http://projecteuclid.org/euclid.facm/1254330158
Zentralblatt MATH identifier: 05635531
Mathematical Reviews number (MathSciNet): MR2568795
Digital Object Identifier: doi:10.7169/facm/1254330158
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