Runovski, K.; Schmeisser, H.-J. On the convergence of Fourier means and interpolation means. (English) Zbl 1079.42001 J. Comput. Anal. Appl. 6, No. 3, 211-227 (2004). Summary: The necessary and sufficient conditions for the convergence of the Fourier means and the interpolation means in \(L_p\) spaces of \(2\pi\)-periodic functions with \(1\leq p \leq +\infty\) are established in terms of the Fourier transform of the kernel generator. It is shown that both methods are equivalent from the point of view of their approximation errors. Some applications of the results obtained are given. Cited in 7 Documents MSC: 42A10 Trigonometric approximation 42A24 Summability and absolute summability of Fourier and trigonometric series Keywords:Fourier means; interpolation; approximation errors; necessary and sufficient conditions for convergence PDF BibTeX XML Cite \textit{K. Runovski} and \textit{H. J. Schmeisser}, J. Comput. Anal. Appl. 6, No. 3, 211--227 (2004; Zbl 1079.42001)