數(shù)域上的傅里葉分析

內(nèi)容概要

　　《數(shù)域上傅里葉分析(英文版)》是一部學(xué)習(xí)數(shù)論和群論的研究生教程。每章的引入也是十分有意思，對歷史材料的深入理解和作者對相關(guān)內(nèi)容獨(dú)到的理解和表達(dá)方式，使得本書組成一個(gè)有機(jī)的整體，這些正是一個(gè)初學(xué)者所需要的。同時(shí)，這本書也很適合于科研人員。書中包括了不少比較復(fù)雜的內(nèi)容，使得這本書的部分內(nèi)容比較難懂，也是本書吸引讀者的一個(gè)原因。每章的后面都附有習(xí)題。
　　讀者對象：數(shù)學(xué)專業(yè)的研究生，教師和相關(guān)專業(yè)的科研人員。

書籍目錄

preface
index of notation
1 topolooical groups
　1.1 basic notions
　1.2 haar measure
　1.3 profinite groups
　1.4 pro-p-groups
　exercises
2 some representation theory
　2.1 representations of locally compact groups
　2.2 banach algebras and the gelfand transform
　2.3 the spectral theorems
　2.4 unitary representations
　exercises
3 duality for locally compact abelian groups
　3.1 the pontryagin dual
　3.2 functions of positive type
　3.3 the fourier inversion formula
　3.4 pontryagin duality
　exercises
4 the structure of arithmetic fields
　4.1 the module of an automorphism
　4.2 the classification of locally compact fields
　4.3 extensions of local fields
　4.4 places and completions of global fields
　4.5 ramification and bases
　exercises
5 adeles, ideles, and the class groups
　5.1 restricted direct products, characters, and measures
　5.2 adeles, ideles, and the approximation theorem
　5.3 the geometry of ak/k
　5.4 the class groups
　exercises
6 a quick tour of class field theory
　6.1 frobenius elements
　6.2 the tchebotarev density theorem
　6.3 the transfer map
　6.4 artin's reciprocity law
　6.5 abelian extensions of q and qr
　exercises
7 tate's thesis and applications
　7.1 local -functions
　7.2 the riemann-roch theorem
　7.3 the global functional equation
　7.4 hecke l-functions
　7.5 the volume of c1k and the regulator
　7.6 dirichlet's class number formula
　7.7 nonvanishing on tile line re(s)=1
　7.8 comparison of hecke l-functions
　exercises
appendices
　appendix a: normed linear spaces
　　a.1 finite-dimensional normed linear spaces
　　a.2 the weak topology
　　a.3 the weak-star topology
　　a.4 a review of lr-spaces and duality
　appendix b: dedekind domains
　　b.1 basic properties
　　b.2 extensions of dedekind domains
references
index

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