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  • 数域上的傅里叶分析(英文)[平装]
  • 共2个商家     33.80元~36.00
  • 作者:罗摩克里希纳(DinakarRamakrishnan)(作者)
  • 出版社:世界图书出版公司;第1版(2011年7月1日)
  • 出版时间:
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  • 包装:
  • ISBN:9787510037511

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    《数域上的傅里叶分析(英文)》由世界图书出版公司出版。

    作者简介

    作者:(美国)罗摩克里希纳 (Dinakar Ramakrishnan)

    目录

    PREFACE
    INDEX OF NOTATION
    TOPOLOGICAL 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. I 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 Ar/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 Qp
    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 C and the Regulator
    7.6 Dirichlet's Class Number Formula
    7.7 Nonvanishing on the Line Re(s)——I
    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-Slat Topology
    A.4 A Review of LP-Spaces and Duality
    Appendix B: Dedekind Domains
    B.1 Basic Properties
    B.2 Extensions of Dedekind Domains
    REFERENCES
    INDEX

    文摘

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