Topological Vector Spaces, Distributions and Kernels

Content: 
Editoral Page
Page v

Copyright Page
Page vi

Preface
Pages ix-xi
François Treves

PART I Topological Vector Spaces. Spaces of Functions
Pages 2-5

1 Filters. Topological Spaces. Continuous Mappings
Pages 6-13

2 Vector Spaces. Linear Mappings
Pages 14-19

3 Topological Vector Spaces. Definition
Pages 20-30

4 Hausdorff Topological Vector Spaces. Quotient Topological Vector Spaces. Continuous Linear Mappings
Pages 31-36

5 Cauchy Filters. Complete Subsets. Completion
Pages 37-49

6 Compact Sets
Pages 50-56

7 Locally Convex Spaces. Seminorms
Pages 57-69

8 Metrizable Topological Vector Spaces
Pages 70-77

9 Finite Dimensional Hausdorff Topological Vector Spaces. Linear Subspaces with Finite Codimension. Hyperplanes
Pages 78-84

10 Fréchet Spaces. Examples
Pages 85-94

11 Normable Spaces. Banach Spaces. Examples
Pages 95-111

12 Hilbert Spaces
Pages 112-125

13 Spaces LF. Examples
Pages 126-135

14 Bounded Sets
Pages 136-149

15 Approximation Procedures in Spaces of Functions
Pages 150-160

16 Partitions of Unity
Pages 161-165

17 The Open Mapping Theorem
Pages 166-173

Part II. Duality. Spaces of Distributions
Pages 176-179

18 The Hahn-Banach Theorem
Pages 181-194

19 Topologies on the Dual
Pages 195-201

20 Examples of Duals among Lp Spaces
Pages 202-215

21 Radon Measures. Distributions
Pages 216-226

22 More Duals: Polynomials and Formal Power Series. Analytic Functionals
Pages 227-239

23 Transpose of a Continuous Linear Map
Pages 240-252

24 Support and Structure of Distribution
Pages 253-266

25 Example of Transpose: Fourier Transformation of Tempered Distributions
Pages 267-277

26 Convolution of Functions
Pages 278-283

27 Example of Transpose: Convolution of Distributions
Pages 284-297

28 Approximation of Distributions by Cutting and Regularizing
Pages 298-304

29 Fourier Transforms of Distributions with Compact Support.
Pages 305-313

30 Fourier Transforms of Convolutions and Multiplications
Pages 314-321

31 The Sobolev Spaces
Pages 322-334

32 Equicontinuous Sets of Linear Mappings
Pages 335-345

33 Barreled Spaces. The Banach-Steinhaus Theorem
Pages 346-350

34 Applications of the Banach-Steinhaus Theorem
Pages 351-359

35 Further Study of the Weak Topology
Pages 360-367

36 Topologies Compatible with a Duality. The Theorem of Mackey. Reflexivity
Pages 368-377

37 Surjections of Fréchet Spaces
Pages 378-386

38 Surjections of Fréchet Spaces (continued). Applications
Pages 387-394

Part III. Tensor Products. Kernels
Pages 396-402

39 Tensor Product of Vector Spaces
Pages 403-410

40 Differentiable Functions with Values in Topological Vector Spaces. Tensor Product of Distributions
Pages 411-419

41 Bilinear Mappings. Hypocontinuity
Pages 420-426

42 Spaces of Bilinear Forms. Relation with Spaces of Linear Mappings and with Tensor Products
Pages 427-433

43 The Two Main Topologies on Tensor Products. Completion of Topological Tensor Products
Pages 434-445

44 Examples of Completion of Topological Tensor Products: Products ε
Pages 446-458

45 Examples of Completion of Topological Tensor Products: Completed π-Product of Two Fréchet Spaces
Pages 459-466

46 Examples of Completion of Topological Tensor Products: Completed π-Product with a Space L1
Pages 467-476

47 Nuclear Mappings
Pages 477-487

48 Nuclear Operators in Hilbert Spaces
Pages 488-499

49 The Dual of E⊗εF. Integral Mappings
Pages 500-508

50 Nuclear Spaces
Pages 509-525

51 Examples of Nuclear Spaces. The Kernels Theorem
Pages 526-534

52 Applications
Pages 535-547

Appendix: The Borel Graph Theorem
Pages 549-558

Index of Notation
Pages 559-560

Subject Index
Pages 561-565