目录： i fourier series on t 1 fourier coefficients 2 summability in norm and homogeneous banach spaces on t 3 pointwise convergence of n(f) 4 the order of magnitude of fourier coefficients 5 fourier series of square summable functions 6 absolutely convergent fourier series 7 fourier coefficients of linear functionals 8 additional comments and applications 9 the d-dimensional torus ii the convergence of fourier series 1 convergence in norm 2 convergence and divergence at a point 3 sets of divergence iii the conjugate function 1 the conjugate function 2 the maximal function of hardy and littlewood 3 the hardy spates iv interpolation of linear operators 1 interpolation of norms and of linear operators .2 the theorem of hausdorff-young 3 marcinkiewicz's theorem v lacunary series and quasi-analytic classes 1 lacunary series 2 quasi-analytic classes vi fourier transforms on the line 1 fourier transforms for l1(r) 2 fourier-stieltjes transforms 3 fourier transforms in lp(r), 1 [ p [ 2 4 tempered distributions and pseudomeasures 5 almost-periodic functions on the line 6 the weak-star spectrum of bounded functions 7 the paley-wiener theorems 8 the fourier-carleman transform 9 kronecker's theorem vii fourier analysis on locally compact abelian groups 1 locally compact abelian groups 2 the haar measure 3 characters and the dual group 4 fourier transforms 5 almost-periodic functions and the bohr compactification viii commutative banach algebras 1 definition, examples, and elementary properties 2 maximal ideals and multiplicative linear functionals 3 the maximal-ideal space and the gelfand representation 4 homomorphisms of banach algebras 5 regular algebras 6 wiener's general tauberian theorem 7 spectral synthesis in regular algebras 8 functions that operate in regular banach algebras 9 the algebra m(t) and functions that operate on fourier-stieltjes coefficients 10 the use of tensor products a vector-valued functions 1 riemann integration 2 improper integrals 3 more general integrals 4 holomorphic vector-valued functions b probabilistic methods 1 random series 2 fourier coefficients of continuous functions 3 paley-zygmund, (when ∑｜an｜2 =∞) bibliography index
