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本書自1968年齣版後，就牢固地樹立瞭其經典地位，並受到學生和專傢們的推崇。Katznelson教授因此書而獲得瞭2002年度的斯提爾奬。

本書從經典傅裏葉分析的清晰錶述入手，旨在用一個具體的構架展示調和分析的中心思想，並提供瞭大量有助於透徹瞭解調和分析理論的例子。作者在確立這些思想之後，轉嚮擴展調和分析，使之遠遠超越圓群的範圍，並通過在實綫上討論傅裏葉變換以及在局部緊阿貝爾群上對傅裏葉分析的簡單考察，打開通嚮其他領域的大門。

與以前的版本相比，本版增加瞭若乾補充材料，其中包括逼近論中的諸多主題和在調和分析中運用概率論方法的一些例子。

Yitzhak Katznelson於巴黎大學獲得博士學位。他曾執教於加州大學伯剋利分校、希伯來大學和耶魯大學，現任斯坦福大學數學教授。他的數學研究領域包括調和分析、遍曆理論和可微分動力係統。

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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