Xie, T. F.; Zhou, S. P. The uniform convergence of certain trigonometric series. (English) Zbl 0791.42004 J. Math. Anal. Appl. 181, No. 1, 171-180 (1994). Summary: A result of J. R. Nurcombe [J. Math. Anal. Appl. 166, No. 2, 577- 581 (1992; Zbl 0756.42006)] giving a necessary and sufficient condition for the uniform convergence of a sine series with quasimonotone coefficients is generalized to certain trigonometric series with complex \(O\)-regularly varying quasimonotone coefficients. Cited in 2 ReviewsCited in 3 Documents MSC: 42A32 Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.) 42A20 Convergence and absolute convergence of Fourier and trigonometric series Keywords:uniform convergence; sine series; quasimonotone coefficients; trigonometric series; complex \(O\)-regularly varying quasimonotone coefficients Citations:Zbl 0756.42006 PDFBibTeX XMLCite \textit{T. F. Xie} and \textit{S. P. Zhou}, J. Math. Anal. Appl. 181, No. 1, 171--180 (1994; Zbl 0791.42004) Full Text: DOI