本書自1968年出版后，就牢固地樹立了其經(jīng)典地位，并受到學(xué)生和專家們的推崇。Katznelson教授因此書而獲得了2002年度的斯提爾獎。
本書從經(jīng)典傅里葉分析的清晰表述入手，旨在用一個具體的構(gòu)架展示調(diào)和分析的中心思想，并提供了大量有助于透徹了解調(diào)和分析理論的例子。作者在確立這些思想之后，轉(zhuǎn)向擴(kuò)展調(diào)和分析，使之遠(yuǎn)遠(yuǎn)超越圓群的范圍，并通過在實(shí)線上討論傅里葉變換以及在局部緊阿貝爾群上對傅里葉分析的簡單考察，打開通向其他領(lǐng)域的大門。
與以前的版本相比，本版增加了若干補(bǔ)充材料，其中包括逼近論中的諸多主題和在調(diào)和分析中運(yùn)用概率論方法的一些例子。
作者簡介
Yitzhak Katznelson于巴黎大學(xué)獲得博士學(xué)位。他曾執(zhí)教于加州大學(xué)伯克利分校、希伯來大學(xué)和耶魯大學(xué)，現(xiàn)任斯坦福大學(xué)數(shù)學(xué)教授。他的數(shù)學(xué)研究領(lǐng)域包括調(diào)和分析、遍歷理論和可微分動力系統(tǒng)。
目錄：
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 =∞)
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