ON THE SUMS OF TRIGONOMETRIC SERIES

Contents § 1. Introduction § 2. Subsidiary material § 3. Elementary facts about the sums of certain series § 4. Differentiability properties § 5. On bounds, intervals of constant sign, and roots of sums of sine-series § 6. Intervals of constant sign and estimates of sums of cosine-series § 7. On monotonicity of sums of sine- and cosine-series § 8. On the roots and intervals of constant sign of sums of a class of general trigonometric series § 9. Representation of sums of absolutely convergent series § 10. On weakly oscillating functions § 11. Asymptotic formulae in the neighbourhood of singular points § 12. Asymptotic formulae in the neighbourhood of singular points for the derivatives of the sums of special series § 13. Various theorems and examples § 14. Unsolved problems and questions References