CHAPTER Ⅰ TRIGONOMETRIC SERIES AND FOURIER SERIES. AUXILIARY RESULTS 1. Trigonometric series 2. Summation by parts 3. Orthogonal series 4. The trigonometric system 5. Fourier-Stieltjes series 6. Completeness of'the trigonometric system 7. Bossel's inequality and Parsoval's formula 8. Remarks on series and integrals 9. Inequalities 10. Convex functions 11. Convergence in Lr 12. Sets of the first and second categories 13. Rearrangements of functions. Maximal theorems of Hardy and Littlewood Miscellaneous theorems and examples
CHAPTER Ⅱ FOURIER COEFFICIENTS. ELEMENTARY THEOREMS ON THE CONVERGENCE OF s[f] AND s[f] 1. Formal operations on s[f] 2. Differentiation and integration of s[f] 3. Modulus of continuity. Smooth functions 4. Order of magnitude of Fourier coefficients 5. Formulae for partial sums of s[f] and s[f] 6. The Dini test and the principle of localization 7. Some more formulae for partial sums 8. The Diriehlet-Jordan test ……
CHAPTER Ⅲ SUMMABILITY OF FOURIES SERIES CHAPTER Ⅳ CLASSES OF FUNCTIONS AND FOURIER SERIES CHAPTER Ⅴ SPECIAL TRIGONOMERIC SERIES CHAPTER Ⅵ THE SBSOLUTE CONVERGENCE OF TRIGONOMETRIC SERIES CHAPTER Ⅶ COMPLEX METHODS IN FOURIER SERIES CHAPTER Ⅷ DIVERGENCE OF FOURIER SERIES CHAPTER Ⅸ RIEMANN'S THEORY OF TRIGONOMETRIC SERIES