三角级数-第1卷-第3版

PrefaceList of SymbolsCHAPTER ⅠTRIGONOMETRIC SERIES AND FOURIER SERIES．AUXILIARY RESULTS1． Trigonometric series2． Summation by parts3． Orthogonal series4． The trigonometric system5． Fourier-Stieltjes series6． Completeness of'the trigonometric system7． Bossel's inequality and Parsoval's formula8． Remarks on series and integrals9． Inequalities10． Convex functions11． Convergence in Lr12． Sets of the first and second categories13． Rearrangements of functions． Maximal theorems of Hardy andLittlewoodMiscellaneous theorems and examplesCHAPTER ⅡFOURIER COEFFICIENTS． ELEMENTARY THEOREMS ONTHE 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 functions4． Order of magnitude of Fourier coefficients5． Formulae for partial sums of s[f] and s[f]6． The Dini test and the principle of localization7． Some more formulae for partial sums8． The Diriehlet-Jordan test…… CHAPTER Ⅲ SUMMABILITY OF FOURIES SERIESCHAPTER Ⅳ CLASSES OF FUNCTIONS AND FOURIER SERIESCHAPTER Ⅴ SPECIAL TRIGONOMERIC SERIESCHAPTER Ⅵ THE SBSOLUTE CONVERGENCE OF TRIGONOMETRIC SERIESCHAPTER Ⅶ COMPLEX METHODS IN FOURIER SERIESCHAPTER Ⅷ DIVERGENCE OF FOURIER SERIESCHAPTER Ⅸ RIEMANN'S THEORY OF TRIGONOMETRIC SERIES