Preface
List of Symbols
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
