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Introduction to Graph Theory2025|PDF|Epub|mobi|kindle电子书版本百度云盘下载

[美]Douglas B.West著著
出版社：机械工业出版社
ISBN：7111152158
出版时间：2004
标注页数：424页
文件大小：15MB
文件页数：437页
主题词：图论－英文

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图书目录

Part Ⅰ General Theory3

1 Topological Vector Spaces3

Introduction3

Separation properties10

Linear mappings14

Finite-dimensional spaces16

Metrization18

Boundedness and continuity23

Seminorms and local convexity25

Quotient spaces30

Examples33

Exercises38

2 Completeness42

Baire category42

The Banach-Steinhaus theorem43

The open mapping theorem47

The closed graph theorem50

Bilinear mappings52

Exercises53

3 Convexity56

The Hahn-Banach theorems56

Weak topologies62

Compact convex sets68

Vector-valued integration77

Holomorphic functions82

Exercises85

4 Duality in Banach Spaces92

The normed dual of a normed space92

Adjoints97

Compact operators103

Exercises111

5 Some Applications116

A continuity theorem116

Closed subspaces of Lp-spaces117

The range of a vector-valued measure120

A generalized Stone-Weierstrass theorem121

Two interpolation theorems124

Kakutani’s fixed point theorem126

Haar measure on compact groups128

Uncomplemented subspaces132

Sums of Poisson kernels138

Two more fixed point theorems139

Exercises144

Part Ⅱ Distributions and Fourier Transforms149

6 Test Functions and Dist butions149

Introduction149

Test function spaces151

Calculus with distributions157

Localization162

Supports of distributions164

Distributions as derivatives167

Convolutions170

Exercises177

7 Fourier Transforms182

Basic properties182

Tempered distributions189

Paley-Wiener theorems196

Sobolev’s lemma202

Exercises204

8 Applications to Differential Equations210

Fundamental solutions210

Elliptic equations215

Exercises222

9 Tauberian Theory226

Wiener’s theorem226

The prime number theorem230

The renewal equation236

Exercises239

Part Ⅲ Banach Algebras and Spectral Theory245

10 Banach Algebras245

Introduction245

Complex homomorphisms249

Basic properties of spectra252

Symbolic calculus258

The group of invertible elements267

Lomonosov’s invariant subspace theorem269

Exercises271

11 Commutative Banach Algebras275

Ideals and homomorphisms275

Gelfand transforms280

Involutions287

Applications to noncommutative algebras292

Positive functionals296

Exercises301

12 Bounded Operators on a Hilbert Space306

Basic facts306

Bounded operators309

A commutativity theorem315

Resolutions of the identity316

The spectral theorem321

Eigenvalues of normal operators327

Positive operators and square roots330

The group of invertible operators333

A characterization of B-algebras336

An ergodic theorem339

Exercises341

13 Unbounded Operators347

Introduction347

Graphs and symmetric operators351

The Cayley transform356

Resolutions of the identity360

The spectral theorem368

Semigroups of operators375

Exercises385

Appendix A Compactness and Continuity391

Appendix B Notes and Comments397

Bibliography412

List of Special Symbols414

Index417