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  • 醉染图书泛函分析(英文版·原书第2版·典藏版)9787111654742
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    • 作者: (美)沃尔特·鲁丁(Walter Rudin)著 | (美)沃尔特·鲁丁(Walter Rudin)编 | (美)沃尔特·鲁丁(Walter Rudin)译 | (美)沃尔特·鲁丁(Walter Rudin)绘
    • 出版社: 机械工业出版社
    • 出版时间:2020-05-01
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    • 作者: (美)沃尔特·鲁丁(Walter Rudin)著| (美)沃尔特·鲁丁(Walter Rudin)编| (美)沃尔特·鲁丁(Walter Rudin)译| (美)沃尔特·鲁丁(Walter Rudin)绘
    • 出版社:机械工业出版社
    • 出版时间:2020-05-01
    • 版次:1
    • 印次:1
    • 页数:424
    • 开本:16开
    • ISBN:9787111654742
    • 版权提供:机械工业出版社
    • 作者:(美)沃尔特·鲁丁(Walter Rudin)
    • 著:(美)沃尔特·鲁丁(Walter Rudin)
    • 装帧:平装
    • 印次:1
    • 定价:99.00
    • ISBN:9787111654742
    • 出版社:机械工业出版社
    • 开本:16开
    • 印刷时间:暂无
    • 语种:暂无
    • 出版时间:2020-05-01
    • 页数:424
    • 外部编号:1202071236
    • 版次:1
    • 成品尺寸:暂无

    Preface

    About the Author

    Part I General Theory

    1 Topological Vector Spaces

    Introduction

    Separation properties

    Linear mappings

    Finite-dimensional spaces

    Metrization

    Boundedness and continuity

    Seminorms and local convexity

    otient spaces

    Examples

    Exercises

    2 Comleess

    Baire category

    The Banach-Steinhaus theorem

    The open mapping theorem

    The closed graph theorem

    Bilinear mappings

    Exercises

    3 Convexity

    The Hahn-Banach theorems

    Weak topologies

    Compact convex sets

    Vector-valued integration

    Holomorphic functions

    Exercises

    4 Duality in Banach Spaces

    The normed dual of a normed space

    Adjoints

    Compact operators

    Exercises

    5 Some Applications

    A continuity theorem

    Closed subspaces of Lp-spaces

    The range of a vector-valued measure

    A generalized Stone-Weierstrass theorem

    Two interpolation theorems

    Kakutanis fixed point theorem

    Haar measure on compact groups

    Uncomplemented subspaces

    Sums of Poisson kernels

    Two more fixed point theorems

    Exercises

    Part Ⅱ Distributions and Fourier Transforms

    6 Test Functions and Distributions

    Introduction

    Test function spaces

    Calculus with distributions

    Localization

    Supports of distributions

    Distributions as derivatives

    Convolutions

    Exercises

    7 Fourier Transforms

    Basic properties

    Tempered distributions

    Paley-Wiener theorems

    Sobolevs lemma

    Exercises

    8 Applications to Differential Equations

    Fundamental solutions

    Elliptic equations

    Exercises

    9 Tauberian Theory

    Wieners theorem

    The prime number theorem

    The renewal equation

    Exercises

    Part Ⅲ Banach Algebras and Spectral Theory

    10 Banach Algebras

    Introduction

    Complex homomorphisms

    Basic properties of spectra

    Symbolic calculus

    The group of invertible elements

    Lomonosovs invariant subspace theorem

    Exercises

    11 Commutative Banach Algebras

    Ideals and homomorphisms

    Gelfand transforms

    Involutions

    Applications to noncommutative algebras

    Positive functionals

    Exercises

    12 Bounded Operators on a Hilbert Space

    Basic facts

    Bounded operators

    A commutativity theorem

    Resolutions of the identity

    The spectral theorem

    Eigenvalues of normal operators

    Positive operators and square roots

    The group of invertible operators

    A characterization of B*-algebras

    An ergodic theorem

    Exercises

    13 Unbounded Operators

    Introduction

    Graphs and symmetric operators

    The Cayley transform

    Resolutions of the identity

    The spectral theorem

    Semigroups of operators

    Exercises

    Appendix A Compactness and Continuity

    Appendix B Notes and Comments

    Bibliography

    List of Spe Symbols

    Index

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