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Topological Vector Spaces, Distributions and Kernels.

Topological vector spaces, distributions and kernels.

Detalles Bibliográficos
Clasificación:	Libro Electrónico
Autor principal:	Treves, Francois
Formato:	Electrónico eBook
Idioma:	Inglés
Publicado:	Burlington : Elsevier, 1967.
Edición:	2nd ed.
Temas:	Functional analysis. Linear topological spaces. Analyse fonctionnelle. Espaces vectoriels topologiques. Functional analysis Linear topological spaces
Acceso en línea:	Texto completo

Tabla de Contenidos:

Front Cover
Topological Vector Spaces, Distributions and Kernels
Copyright Page
Contents
Preface
Part I: Topological Vector Spaces. Spaces of Functions
Chapter 1. Filters. Topological Spaces. Continuous Mappings
Chapter 2. Vector Spaces. Linear Mappings
Chapter 3. Topological Vector Spaces. Definition
Chapter 4. Hausdorff Topological Vector Spaces. Quotient Topological Vector Spaces. Continuous Linear Mappings
Hausdorff Topological Vector Spaces
Quotient Topological Vector Spaces
Continuous Linear Mappings.
Chapter 5. Cauchy Filters. Complete Subsets. Completion
Chapter 6. Compact Sets
Chapter 7. Locally Convex Spaces. Seminorms
Chapter 8. Metrizable Topological Vector Spaces
Chapter 9. Finite Dimensional Hausdorff Topological Vector Spaces. Linear Subspaces with Finite Codimension. Hyperplanes
Chapter 10. Fréchet Spaces. Examples
Example I. The Space of ℓk Functions in an Open Subset of Rn
Example II. The Space of Holomorphic Functions in an Open Subset of Cn
Example III. The Space of Formal Power Series in n Indeterminates.
Example IV. The Space e of e Functions in Rn Rapidly Decreasing at Infinity
Chapter 11. Normable Spaces. Banach Spaces. Examples.
Chapter 12. Hilbert Spaces
Chapter 13. Spaces LF. Examples
Chapter 14. Bounded Sets
Chapter 15. Approximation Procedures in Spaces of Functions
Chapter 16. Partitions of Unity
Chapter 17. The Open Mapping Theorem
Part II: Duality. Spaces of Distributions
Chapter 18. The Hahn-Banach Theorem
(1) Problems of Approximation
(2) Problems of Existence
(3) Problems of Separation
Chapter 19. Topologies on the Dual.
Chapter 20. Examples of Duals among Lp Spaces
Example I. The Duals of the Spaces of Sequences lp(1 {600} p <+)
Example II. The Duals of the Spaces Lp() (1 {600} p <+)
Chapter 21. Radon Measures. Distributions
Radon Measures in an Open Subset of Rn
Distributions in an Open Subset of Rn
Chapter 22. More Duals: Polynomials and Formal Power Series. Analytic Functionals
Polynomials and Formal Power Series
Analytic Functionals in an Open Subset of Cn
Chapter 23. Transpose of a Continuous Linear Map
Example I. Injections of Duals.
Example II. Restrictions and Extensions
Example III. Differential Operators
Chapter 24. Support and Structure of a Distribution
Distributions with Support at the Origin
Chapter 25. Example of Transpose: Fourier Transformation of Tempered Distributions
Chapter 26. Convolution of Functions
Chapter 27. Example of Transpose: Convolution of Distributions
Chapter 28. Approximation of Distributions by Cutting and Regularizing
Chapter 29. Fourier Transforms of Distributions with Compact Support The Paley-Wiener Theorem.

Topological Vector Spaces, Distributions and Kernels.

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