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.
Primary Subjects: 42A10
Secondary Subjects: 42A15, 42B15
Keywords: approximation; trigonometric polynomials; Lp-convergence; classical means; Fourier transform
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Permanent link to this document: http://projecteuclid.org/euclid.facm/1254330158
Functiones et Approximatio Commentarii Mathematici
