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The uniform convergence of certain trigonometric series. (English) Zbl 0791.42004
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.

MSC:
 42A32 Trigonometric series of special types (positive coefficients, monotonic coefficients, etc.) 42A20 Convergence and absolute convergence of Fourier and trigonometric series
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