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
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